Disorder solutions for the partition functions of the two-dimensional Ising-like models

2020/11/20 by Pavel Khrapov, Khrapov, Pavel
Mathematics · Physics and Astronomy · #82B20 #82B23 #FOS: Physical sciences #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #msc:82B20 #msc:82B23

paper · pdf · doi:10.48550/arxiv.2011.10259

39 pages

openalex publication_date 2020/11/20 · arxiv created 2020/11/23 · arxiv updated 2020/11/24 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

For the generalized Ising models with all possible interactions within a face of the square lattice the formulas for finding partition function and free energy per lattice site in the thermodynamic limit were derived on a certain, in the general case, 8-dimensional subset of exact disordered solutions of 10-dimensional set of the Hamiltonian's parameters. When a part of parameters are set to zero, as a consequence, the disorder solutions were got for the models with nearest, next-nearest-neighbor and the interaction of four spins in an external field and without an external field, triangular and "checkerboard-triangular" Ising models with triple interactions in an external magnetic field.

Related

• Disorder solutions for generalized 2D Ising Model with multi-spin interaction
• Disorder solutions for the free energy of the Ising-like models
• Form of the exact partition function for the generalized Ising Model
• Partition function for the two-dimensional square lattice Ising model in a non-zero magnetic field-A heuristic analysis
• Partition Function for Two-Dimensional Nearest Neighbour Ising Model in a Non-Zero Magnetic Field for a Square Lattice of 16 Sites