The statistics of dimers on a lattice

From MaRDI portal
Publication:2903673

DOI10.1016/0031-8914(61)90063-5zbMath1244.82014OpenAlexW1653035750WikidataQ29544402 ScholiaQ29544402MaRDI QIDQ2903673

P. W. Kasteleyn

Publication date: 11 August 2012

Published in: Physica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0031-8914(61)90063-5



Related Items

Domino statistics of the two-periodic Aztec diamond, A maximum resonant set of polyomino graphs, A minimax result for perfect matchings of a polyomino graph, The Yang-Baxter equations and the Zamolodchikov model, Enumeration of hybrid domino-lozenge tilings. II: Quasi-octagonal regions, Perfect matchings in random polyomino chain graphs, Miquel dynamics, Clifford lattices and the dimer model, Bipartite dimer representation of squares of 2d-Ising correlations, The emerging role of number theory in exactly solvable models in lattice statistical mechanics, Critical surface of the hexagonal polygon model, On the theory of matchgate computations, Grid graphs, Gorenstein polytopes, and domino stackings, Domino tiling congruence modulo 4, On blockwise symmetric signatures for matchgates, Fundamental constants in the theory of two-dimensional uniform spanning trees, Some remarks on a generalization of the superintegrable chiral Potts model, Elementary components of essentially disconnected polyomino graphs, Matrix models from operators and topological strings. II, On the asymptotics of dimers on tori, Quadri-tilings of the plane, The NP-completeness of a tomographical problem on bicolored domino tilings, Independence entropy of \(\mathbb{Z}^{d}\)-shift spaces, Partition function of periodic isoradial dimer models, Pfaffian graphs embedding on the torus, Matching measure, Benjamini-Schramm convergence and the monomer-dimer free energy, The complexity of generalized domino tilings, Holographic algorithms: from art to science, The cubical matching complex, Solution of the monomer-dimer model on locally tree-like graphs. Rigorous results, Dimer representations of the Temperley-Lieb algebra, The critical \(Z\)-invariant Ising model via dimers: Locality property, Negation can be exponentially powerful, Arctic circles, domino tilings and square Young tableaux, Exact solution of the 2d dimer model: corner free energy, correlation functions and combinatorics, A lower bound on the number of elementary components of essentially disconnected generalized polyomino graphs, Topics on abelian spin models and related problems, Discrete Dirac operators on Riemann surfaces and Kasteleyn matrices, Counting dimer coverings on self-similar Schreier graphs, Monte Carlo simulations for quantum field theories involving fermions, Signature theory in holographic algorithms, The fermionic observable in the Ising model and the inverse Kac-Ward operator, Onsager and Kaufman's calculation of the spontaneous magnetization of the Ising model, Dimers belonging to three orientations on plane honeycomb lattices, Dimer coverings on the Sierpinski gasket, A collapse theorem for holographic algorithms with matchgates on domain size at most 4, Spotlight tiling, The Pfaffian property of circulant graphs, Random skew plane partitions with a piecewise periodic back wall, The symbiotic relationship of combinatorics and matrix theory, Face-width of Pfaffian braces and polyhex graphs on surfaces, Combinatorial analysis of tetris-like games, Matchings in vertex-transitive bipartite graphs, Minimally non-Pfaffian graphs, Pfaffian graphs, \(T\)-joins and crossing numbers, Pfaffian labelings and signs of edge colorings, An expression for the perfect matching number of cubic \(2\times m\times n\) lattices and their asymptotic values, How to calculate the number of perfect matchings in finite sections of certain infinite plane graphs, Tiling problems, automata, and tiling graphs, Matching theory -- a sampler: From Dénes König to the present, Alternating-sign matrices and domino tilings. II, Pfaffian correlation functions of planar dimer covers, Spin systems on \(k\)-regular graphs with complex edge functions, Maximum matchings in scale-free networks with identical degree distribution, Alternating-sign matrices and domino tilings. I, Approximating the hard square entropy constant with probabilistic methods, An asymptotic expansion and recursive inequalities for the monomer-dimer problem, On symmetric signatures in holographic algorithms, Local statistics of realizable vertex models, On the number of Kekulé structures in capped zigzag nanotubes, The critical \(Z\)-invariant Ising model via dimers: the periodic case, Nearly tight bounds on the number of Hamiltonian circuits of the hypercube and generalizations, A bijection theorem for domino tilings with diagonal impurities, On the expressive power of permanents and perfect matchings of matrices of bounded pathwidth/cliquewidth, The number of perfect matchings in a hypercube, The Pfaffian sign theorem for the dimer model on a triangular lattice, A Pfaffian formula for the monomer-dimer model on surface graphs, Generalizing the divisibility property of rectangle domino tilings, Efficiently computing the permanent and Hafnian of some banded Toeplitz matrices, Statistical mechanics models and the modular group, Enumeration of dimer (domino) configurations, Double handled brane tilings, The combinatorics of N. G. de Bruijn, A binomial approximation method for the Ising model, On the validations of the asymptotic matching conjectures, Dimers on graphs in non-orientable surfaces, Holographic algorithms: the power of dimensionality resolved, Computation of terms in the asymptotic expansion of dimer \(\lambda_d\) for high dimension, Approximating the permanent via importance sampling with application to the dimer covering problem, Loop statistics in the toroidal honeycomb dimer model, Relaxation time for a dimer covering with height representation, Domino tilings of Aztec diamonds and squares, Sequential cavity method for computing free energy and surface pressure, A note on the occupational degeneracy for dimers on a saturated two- dimensional lattice space, Fluxes, Laplacians, and Kasteleyn's theorem, Complete integrability in statistical mechanics and the Yang-Baxter equations, Exact solution of a vertex model in \(d\) dimensions, A statistical model of current loops and magnetic monopoles, Odd \(K_{3,3}\) subdivisions in bipartite graphs, Walks, walls, wetting, and melting, Planar dimers and Harnack curves, GENERALIZED DOMINOES TILING'S MARKOV CHAIN MIXES FAST, Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so2n+1 *, On the connectivity of spaces of three-dimensional domino tilings, On Wiener index and Wiener polarity index of some polyomino chains, Double interlacing in random tiling models, Perfect matchings, rank of connection tensors and graph homomorphisms, Local correlation functions of the two-periodic weighted Aztec diamond in mesoscopic limit, Weighted graphs, spanning tree generating functions and anisotropic lattice systems: illustrative results for the Ising and dimer models, The two-point correlation function in the six-vertex model, Criteria for a Structure to be Mesoionic, Exact finite-size corrections in the dimer model on a planar square lattice, DIMERS AND SPANNING TREES: SOME RECENT RESULTS, Counting Small Induced Subgraphs Satisfying Monotone Properties, Holographic Algorithm with Matchgates Is Universal for Planar \#CSP over Boolean Domain, Classification of a Class of Counting Problems Using Holographic Reductions, Pfaffian and decomposable numerical range of a complex skew symmetric matrix, Unnamed Item, Toeplitz Matrices and Toeplitz Determinants under the Impetus of the Ising Model: Some History and Some Recent Results, Statistical Mechanics of Dimers on a Plane Lattice. II. Dimer Correlations and Monomers, Unnamed Item, The 16-vertex model and its even and odd 8-vertex subcases on the square lattice, Random sequential covering, Elliptic dimers on minimal graphs and genus 1 Harnack curves, A complete proof that square ice entropy is, Exclusion statistics and thermodynamics of a straight \(k\)-mers lattice-gas: analytical approximation and Monte Carlo simulations, On enumeration and entropy of ribbon tilings, Asymptotics of pure dimer coverings on rail yard graphs, Exact coefficients of finite-size corrections in the Ising model with Brascamp–Kunz boundary conditions and their relationships for strip and cylindrical geometries, Isoradial immersions, The inverse spectral map for dimers, Matchings on trees and the adjacency matrix: A determinantal viewpoint, Disordered monomer-dimer model on cylinder graphs, Weakly nonplanar dimers, A heuristic approach to domino grid problem, The number of ribbon tilings for strips, Interview with Xavier Viennot, Commuting quantum circuits and complexity of Ising partition functions, The monopole-dimer model for Cartesian products of graphs: extended abstract, Holographic algorithms on domains of general size, A complexity trichotomy for \(k\)-regular asymmetric spin systems using number theory, Yang–Baxter solution of dimers as a free-fermion six-vertex model, Dimers, webs, and local systems, Macroscopic loops in the \(3 d\) double-dimer model, The Schwarzian octahedron recurrence (dSKP equation) I: explicit solutions, Five-vertex model and Lozenge tilings of a hexagon with a dent, Counting Small Induced Subgraphs with Hereditary Properties, On the domino shuffle and matrix refactorizations, Undirected determinant and its complexity, GOE fluctuations for the maximum of the top path in alternating sign matrices, The projective fundamental group of a ℤ2-shift, Scaling limits and universality of Ising and dimer models, Beyond windability: approximability of the four-vertex model, The monopole-dimer model on Cartesian products of plane graphs, Phase diagram of the triangular-lattice Potts antiferromagnet, Unnamed Item, Counting Tilings by Taking Walks in a Graph, Isomorphism of dimer configurations and spanning trees on finite square lattices, Affine dimers from characteristic polygons, Model Reductions for Inference: Generality of Pairwise, Binary, and Planar Factor Graphs, Unnamed Item, Minimal free resolutions of 2 × n domino tilings, A Complexity Trichotomy for k-Regular Asymmetric Spin Systems Using Number Theory, On the Complexity of Holant Problems, The 1-2 model, Symmetries of shamrocks IV: The self-complementary case, MUTUALLY-RECURSIVE FORMULAS FOR ENUMERATING PARTITIONS OF THE RECTANGLE, Dimers on Rectangular Lattices, Monomer-dimer problem on random planar honeycomb lattice, ON THE SPATIAL ENTROPY OF TWO-DIMENSIONAL GOLDEN MEAN, Applicability of the Pfaffian Method to Combinatorial Problems on a Lattice, The asymptotic determinant of the discrete Laplacian, Holographic Algorithms with Matchgates Capture Precisely Tractable Planar #CSP, Close-packed dimers on nonorientable surfaces, Dimers and the critical Ising model on lattices of genus \(>1\), Counting domino tilings of rectangles via resultants, Dimer model: Full asymptotic expansion of the partition function, Non-integrable dimer models: Universality and scaling relations, A matrix model for plane partitions, Dimer coverings on the Tower of Hanoi graph, Tilings, Tilings, The geometry of dimer models, The number of matchings in random graphs, Two-dimensional spanning webs as (1, 2) logarithmic minimal model, High-performance sampling of generic determinantal point processes, Topology by Design in Magnetic Nano-materials: Artificial Spin Ice, Matrix permanent and quantum entanglement of permutation invariant states, Yang–Baxter integrable dimers on a strip, A Pfaffian formula for the Ising partition function of surface graphs, Multiplicative degree based topological indices of some chemical structures in drug, Dimers and families of Cauchy-Riemann operators I, Pfaffian Pairs and Parities: Counting on Linear Matroid Intersection and Parity Problems, Historical Face of Number Theory(ists) at the Turn of the 19th Century, Maximal matchings in polyspiro and benzenoid chains, The square lattice Ising model on the rectangle III: Hankel and Toeplitz determinants, Conformal invariance of domino tiling., Remark on the dimer problem, Perfect matchings and perfect squares, Dimer problem for some three dimensional lattice graphs, Dimers on the \(3^3 . 4^2\) lattice, Configurational entropy of a set of dipoles placed on a two-dimensional lattice, Symmetries of plane partitions and the permanent-determinant method, Enumeration of matchings in complete \(q\)-ary trees, On blockwise symmetric matchgate signatures and higher domain \#CSP, Statistics of close-packed dimers on fractal lattices, Spaces of domino tilings, Drawing 4-Pfaffian graphs on the torus, Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices, Spanning trees, cycle-rooted spanning forests on discretizations of flat surfaces and analytic torsion, Conway's influence on the study of random tilings, Regularized limit of determinants for discrete tori, Dimer coverings of 1-slab cubic lattices, Upper bounds on the growth rates of independent sets in two dimensions via corner transfer matrices, Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians, Dimers, networks, and cluster integrable systems, Perfect matchings of cellular graphs, Lozenge tilings of hexagons with cuts and asymptotic fluctuations: a new universality class, Perfect matchings of polyomino graphs, Expressions for the perfect matching numbers of cubic \(l\times m\times n\) lattices and their asymptotic values, Study of dimer-monomer on the generalized Hanoi graph, Sampling weighted perfect matchings on the square-octagon lattice, Simulation strategies for the massless lattice Schwinger model in the dual formulation, Holographic reduction, interpolation and hardness, Site monotonicity and uniform positivity for interacting random walks and the spin \(O(N)\) model with arbitrary \(N\), Limit shapes and local statistics for the stochastic six-vertex model, Tiling-based models of perimeter and area, Dimers and imaginary geometry, Holographic algorithms by Fibonacci gates, A sufficient condition for Pfaffian graphs on the torus, Squareness for the monopole-dimer model, The number of Kekulé structures of polyominos on the torus, Tile invariants: New horizons., Perfect matchings in random pentagonal chains, The Pfaffian property of Cayley graphs on dihedral groups, Tilings of quadriculated annuli, Asymptotic expansions for \(\lambda _{d }\) of the dimer and monomer-dimer problems, Billiards, channels, and perfect matching 2-divisibility, Pólya convertibility problem for symmetric matrices, Towards a theory of frustrated degeneracy., From cycle rooted spanning forests to the critical Ising model: an explicit construction, \(sl(N)\) Onsager's algebra and integrability, On the construction of graphs with a planar bipartite double cover from Boolean formulas and its application to counting satisfying solutions, Holographic algorithms beyond matchgates, Pfaffian polyominos on the Klein bottle, Forcing and anti-forcing polynomials of perfect matchings for some rectangle grids, \(Z\)-transformation graphs of perfect matchings of plane bipartite graphs, Finite-size correction to the scaling of free energy in the dimer model on a hexagonal domain, The nearest-neighbor resonating-valence bond state in a Grassmannian form., Critical free energy of a Möbius strip, Dimer statistics on the Möbius strip and the Klein bottle, Stationary determinantal processes: phase multiplicity, Bernoullicity, entropy, and domination, Coadsorption of monomers and dimers with first neighbour interactions on square lattices, State matrix recursion method and monomer-dimer problem, An improved upper bound for the \(3\)-dimensional dimer problem, Local limits of lozenge tilings are stable under bounded boundary height perturbations, A bijective proof of Macdonald's reduced word formula, Binomial ideals of domino tilings, An \(O(|E(G)|^2)\) algorithm for recognizing Pfaffian graphs of a type of bipartite graphs, Arctic boundaries of the ice model on three-bundle domains, Dimers in piecewise Temperleyan domains, Critical temperature of periodic Ising models, The critical Ising model via Kac-Ward matrices, The height fluctuations of an off-critical dimer model on the square grid, The complexity of planar Boolean \#CSP with complex weights, The Pfaffian property of Cartesian products of graphs, The work of Mike Hochman on multidimensional symbolic dynamics and Borel dynamics, Permutations with restricted movement, Dominos in hedgehog domains, Dichotomy for Holant\(^\ast\) problems on the Boolean domain, Parameterized counting of partially injective homomorphisms, Channels, billiards, and perfect matching 2-divisibility, A generalisation of the honeycomb dimer model to higher dimensions, The \(Z\)-Dirac and massive Laplacian operators in the \(Z\)-invariant Ising model, A polyomino tiling problem of Thurston and its configurational entropy, Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk, Local statistics for random domino tilings of the Aztec diamond, Pfaffian pairs and parities: counting on linear matroid intersection and parity problems, Scaling matrices and counting the perfect matchings in graphs, On dimer coverings of rectangles of fixed width, Matchings in graphs on non-orientable surfaces, A formula for boundary correlations of the critical Ising model, The effect of microscopic gap displacement on the correlation of gaps in dimer systems, Spin chains viewed as the fermionic parts of supersymmetric quantum mechanical models., FKT is not universal -- a planar holant dichotomy for symmetric constraints, Strip tiling and regular grammars, Plane elementary bipartite graphs, Solvable models in statistical mechanics, from Onsager onward., \(\text{sl}(N)\) Onsager's algebra and integrability., Approximating the number of monomer-dimer coverings of a lattice., Computation of sparse circulant permanents via determinants, Singular polynomials of generalized Kasteleyn matrices, A strip-like tiling algorithm, Enumeration of Lozenge tilings of hexagons with cut-off corners, Extending matchings in graphs: A survey, Some exactly solvable and tunable frustrated spin models, An effective algorithm for obtaining polynomials for dimer statistics. Application of operator technique on the topological index to two- and three-dimensional rectangular and torus lattices, Belief propagation and loop series on planar graphs, A new simple proof of the Aztec diamond theorem, Monte Carlo algorithms for computing \(\alpha \)-permanents, The \(C\)-finite ansatz, The topological strong spatial mixing property and new conditions for pressure approximation, Generalized expression for the numbers of perfect matching of cylindrical m×n graphs, Valiant's holant theorem and matchgate tensors, Computational complexity of counting problems on 3-regular planar graphs, Capacity of Higher-Dimensional Constrained Systems, Distances in Domino Flip Graphs, Spectral curves of periodic Fisher graphs, A conjecture of Norine and Thomas for abelian Cayley graphs, \(1/n\) expansion for the number of matchings on regular graphs and Monomer-Dimer entropy, Results and questions on matchings in abelian groups and vector subspaces of fields, Perfect matchings of trimmed Aztec rectangles, The \(Z\)-invariant Ising model via dimers, The Pfaffian property of graphs on the Möbius strip based on topological resolution, Critical varieties in the Grassmannian, Perfect matchings on a type of lattices with toroidal boundary, The 3D dimer and Ising problems revisited, Two counterparts of the TFK formula for cylinder graphs, New directions in algebraic dynamical systems, Pfaffian orientations for a type of bipartite graph, Minimal bipartite dimers and higher genus Harnack curves, Enumeration of perfect matchings of the Cartesian products of graphs, Domino tilings and flips in dimensions 4 and higher, Conformal invariance of loops in the double-dimer model, A variational principle for domino tilings, Coupling functions for domino tilings of Aztec diamonds, Using edge generating function to solve monomer-dimer problem, The free-fermion eight-vertex model: couplings, bipartite dimers and \(Z\)-invariance, The free energies of six-vertex models and the n-equivalence relation, Statistical Matching Theory, An SMB approach for pressure representation in amenable virtually orderable groups, Mean-Field Monomer-Dimer Models. A Review, Perfect matchings in random octagonal chain graphs, Nonequilibrium dynamics of fully frustrated Ising models atT= 0, Some comments on developments in exact solutions in statistical mechanics since 1944, Refined conformal spectra in the dimer model, Rényi entanglement entropies in quantum dimer models: from criticality to topological order, Topological transition in disordered planar matching: combinatorial arcs expansion, Emptiness formation probability, Toeplitz determinants, and conformal field theory, The hypergeometric series for the partition function of the 2D Ising model, Identities between dimer partition functions on different surfaces, Entanglement entropy of local operators in quantum Lifshitz theory, Haldane relation for interacting dimers, Histogram-based methodology for the determination of the critical point in condensation-evaporation systems, Fractionally charged anyons generated by topological path fusion of propagating electron in magnetic flux lattice, CRYSTAL MELTING AND WALL CROSSING PHENOMENA, An optimal algorithm to generate tilings, The Potts model and the Tutte polynomial, Long-range properties of spanning trees, Dimer packings with gaps and electrostatics, On the Monomer–Dimer Problem of Some Graphs, Matchgates and classical simulation of quantum circuits, Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori, Random bichromatic matchings, Lambda-determinants and domino-tilings, Aztec diamonds and digraphs, and Hankel determinants of Schröder numbers, King and domino polynomials for polyomino graphs, Sandpiles and dominos, Exact formulas for 2 × n arrays of dumbbells, Perfect matchings of generalized polyomino graphs, Unnamed Item, Domino tilings and Aztec stars, Mutation of frozen Jacobian algebras, The expectation value of the number of loops and the left-passage probability in the double-dimer model, Pfaffian orientations and perfect matchings of scale-free networks, Quantum matchgate computations and linear threshold gates, The Complexity of Acyclic Subhypergraph Problems, I-tromino tilings of holey squares, On the asymptotic enumeration of restricted strip arrangements of a chessboard, Toric quiver asymptotics and Mahler measure: \( \mathcal{N}=2 \) BPS states, Generalized expression of the perfect matching number for 2×3×n lattices, History and Introduction to Polygon Models and Polyominoes, Exact Entropy of Dimer Coverings for a Class of Lattices in Three or More Dimensions, CONFIGURATIONAL ENTROPY IN GENERALIZED LATTICE-GAS MODELS, Mixing time of Markov chains for the 1-2 model, Theory of computation of multidimensional entropy with an application to the monomer-dimer problem, Solvability of Some Statistical Mechanical Systems, Spanning trees and dimer problem on the Cairo pentagonal lattice, Enumeration of perfect matchings of lattice graphs by Pfaffians, The reconstruction of a subclass of domino tilings from two projections, DIMERS ON TWO-DIMENSIONAL LATTICES, Enumeration of hybrid domino-lozenge tilings, Mahler's Measure and Special Values of L-functions, How quickly can we sample a uniform domino tiling of the \(2L\times 2L\) square via Glauber dynamics?, On the entropy of spanning trees on a large triangular lattice, On a link between Dirichlet kernels and central multinomial coefficients, On 2-adic behavior of the number of domino tilings on torus, Asymptotic domino statistics in the Aztec diamond, Reconstruction of low degree domino tilings, Ribbon tile invariants, Perfect Matchings of the Small Polyominoes, Tacnode GUE-minor processes and double Aztec diamonds, Flip invariance for domino tilings of three-dimensional regions with two floors, Asymptotics of height change on toroidal Temperleyan dimer models, Entropies realizable by block gluing \(\mathbb{Z}^{d}\) shifts of finite type, Convertible andm-convertible matrices