A General Method for Obtaining a Lower Bound for the Ground State Entropy Density of the Ising Model With Short Range Interactions

TL;DR

This paper introduces a universal approach to estimate the minimum ground state entropy density in the Ising Model with short-range interactions, applicable to various 2D lattices and boundary conditions.

Contribution

The paper develops a general method for lower bounding the ground state entropy density in the Ising Model, extending to different lattice types and boundary conditions.

Findings

Lower bounds for the ground state entropy density on square, triangular, and hexagonal lattices.

Method applicable to various boundary conditions including free, cylindrical, and toroidal.

Provides a systematic way to estimate residual entropy in these models.

Abstract

We present a general method for obtaining a lower bound for the ground state entropy density of the Ising Model with nearest neighbor interactions. Then, using this method, and with a random coupling constant configuration, we obtain a lower bound for the ground state entropy density of the square, triangular, and hexagonal two-dimensional lattices with free, cylindrical, and toroidal boundary conditions.