The diagonal two-point correlations of the Ising model on the anisotropic triangular lattice and Garnier systems
DOI10.1088/0951-7715/29/1/131zbMath1338.34170arXiv1504.07214OpenAlexW3104795411MaRDI QIDQ3466418
Publication date: 1 February 2016
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1504.07214
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Additive difference equations (39A10) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)
Cites Work
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- Quasi-periodic solutions of the integrable dynamical systems related to Hill's equation
- The Ising susceptibility scaling function
- Exact enumeration of the ground states of a triangular Ising antiferromagnet
- Bi-orthogonal polynomials on the unit circle, regular semi-classical weights and integrable systems
- Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
- Discrete Painlevé equations and their appearance in quantum gravity
- Rational surfaces associated with affine root systems and geometry of the Painlevé equations
- Solution of the 2D Ising model on a triangular lattice by the method of auxiliary \(q\)-deformed Grassmann fields
- Ground states of the antiferromagnetic Ising model on finite triangular lattices of simple shape
- Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
- A connection between the Henon-Heiles system and the Garnier system
- Some new integrable equations from the self-dual Yang-Mills equations
- ADM approach to \(2+1\) dimensional gravity coupled to particles
- On the polynomial Hamiltonian structure of the Garnier systems
- Polynomials defined by a difference system
- Biorthogonal Systems on the Unit Circle, Regular Semiclassical Weights, and the Discrete Garnier Equations
- Degeneration through coalescence of theq-Painlevé VI equation
- On Discrete Painlevé Equations Associated with the Lattice KdV Systems and the Painlevé VI Equation
- Fredholm determinants, Jimbo‐Miwa‐Ueno τ‐functions, and representation theory
- Application of theτ-function theory of Painlevé equations to random matrices:PVI, the JUE, CyUE, cJUE and scaled limits
- Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model
- Discrete Painlevé equations for a class of PVIτ-functions given asU(N)averages
- Crystal Statistics of a Two-Dimensional Triangular Ising Lattice
- Antiferromagnetism. The Triangular Ising Net
- Crystal Statistics of a Two-Dimensional Ising Lattice
- Statistical mechanics of the two-dimensional assembly
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