Block-diagonalizable two-dimensional generalized Ising systems (BD2DGIS): the free energy

TL;DR

This paper extends a matrix model approach for 2D generalized Ising systems, analyzing its properties under light block diagonalization, and provides exact partition functions and free energy calculations for specific cases.

Contribution

It introduces a detailed analysis of the model's properties under light block diagonalization and derives exact partition functions for a specific 2D generalized Ising system.

Findings

Free energy is independent of the number of rows with many cells.

Exact partition function is obtained for the example with light boundary conditions.

Specific free energy per spin is calculated and visualized.

Abstract

The paper is a continuation of arXiv:2012.10364, where the approach was developed to constructing the exact matrix model for any generalized Ising system, and such model was constructed for certain 2d system. In this paper, the properties of the model are specified for light block diagonalization. A corresponding example is considered. For the example, general exact partition function is obtained and analysed. The analysis shows that the free energy does not depend on the amount of rows with a large amount of cells. For the example with light boundary conditions, the partition function is obtained and the specific free energy per spin is plotted.