Spanning forests and the \(q\)-state Potts model in the limit \(q \to 0\)

DOI10.1007/s10955-005-4409-yzbMath1122.82008arXivcond-mat/0401026OpenAlexW2069085695WikidataQ56893194 ScholiaQ56893194MaRDI QIDQ2574168

Alan D. Sokal, Jesús Salas, Jesper Lykke Jacobsen

Publication date: 18 November 2005

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0401026

zbMATH Keywords

conformal field theorytransfer matrixphase transitiontriangular latticePotts modelBeraha-Kahane-Weiss theoremFortuin-Kasteleyn representationsquare latticeBerker-Kadanoff phasespanning forest

Mathematics Subject Classification ID

Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items

Transfer matrices and partition-function zeros for antiferromagnetic Potts models. V. Further results for the square-lattice chromatic polynomial, The arboreal gas and the supersphere sigma model, Complex-temperature phase diagram of Potts and RSOS models, The antiferromagnetic transition for the square-lattice Potts model, Counting rooted spanning forests for circulant foliation over a graph, Dualities between fermionic theories and the Potts model, Non-scalar operators for the Potts model in arbitrary dimension, Phase diagram of the triangular-lattice Potts antiferromagnet, Critical behaviour of spanning forests on random planar graphs, The ABC (in any D) of logarithmic CFT, Spanning forests andOSP(N|2M) -invariantσ-models, Asymptotic behavior of spanning forests and connected spanning subgraphs on two-dimensional lattices, Phase diagram of the chromatic polynomial on a torus, Renormalization flow for unrooted forests on a triangular lattice, Potts model partition functions on two families of fractal lattices, ARNOLD TONGUES AND FEIGENBAUM EXPONENTS OF THE RATIONAL MAPPING FOR Q-STATE POTTS MODEL ON RECURSIVE LATTICE: Q < 2

Uses Software

• ARPACK
• MPSolve
• OEIS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
• The antiferromagnetic transition for the square-lattice Potts model
• Zeroes of chromatic polynomials: A new approach to Beraha conjecture using quantum groups
• On the universality of the nonphase transition singularity in hard- particle systems
• Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas
• First-order transitions in one-dimensional systems with local couplings
• One-dimensional chiral models with first-order phase transitions
• Logarithmic corrections and finite-size scaling in the two-dimensional 4-state Potts model
• Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem
• Forests, colorings and acyclic orientations of the square lattice
• Critical behaviour of random-bond Potts models: A transfer matrix study
• Flow polynomials and their asymptotic limits for lattice strip graphs
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. III: Triangular-lattice chromatic polynomial
• Reliability polynomials and their asymptotic limits for families of graphs
• Branched polymers and dimensional reduction
• Design, analysis, and implementation of a multiprecision polynomial rootfinder
• Enumeration of \(m\)-ary cacti
• Exact Potts model partition functions for strips of the square lattice
• Exact Potts model partition functions for strips of the triangular lattice
• The three-state square-lattice Potts antiferromagnet at zero temperature.
• Dimensional reduction formulas for branched polymer correlation functions
• Random-cluster measures and uniform spanning trees
• Exact partition functions and correlation functions of multiple Hamiltonian walks on the Manhattan lattice.
• Antiferromagnetic Potts models on the square lattice: A high-precision Monte Carlo study
• Regularity properties and pathologies of position-space renormalization-group transformations: scope and limitations of Gibbsian theory
• On the entropy of spanning trees on a large triangular lattice
• Critical Behavior of Branched Polymers and the Lee-Yang Edge Singularity
• The Potts model and the Tutte polynomial
• Roots of the Reliability Polynomials
• Limits of zeroes of recursively defined polynomials
• A logical expansion in mathematics
• Zeros of Reliability Polynomials and f-vectors of Matroids
• Chromatic Roots are Dense in the Whole Complex Plane
• Three-Colorings of the Square Lattice: A Hard Squares Model
• Asymptotic Enumeration of Spanning Trees
• Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation
• Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model
• A Contribution to the Theory of Chromatic Polynomials
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• Chromatic polynomials and their zeros and asymptotic limits for families of graphs
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. I: General theory and square-lattice chromatic polynomial.
• Transfer matrices and partition-function zeros for antiferromagnetic Potts models. II: Extended results for square-lattice chromatic polynomial.
• Unusual corrections to scaling in the 3-state Potts antiferromagnet on a square lattice.