Estimation of Magnetization, Susceptibility and Specific heat for the two-dimensional Ising Model in a Non-zero Magnetic field

TL;DR

This paper derives partition functions for the 2D Ising model with a magnetic field, introduces a recurrence relation, and estimates magnetization, susceptibility, and critical temperature for infinite lattices.

Contribution

It presents a new recurrence relation valid for all lattice sizes and a novel method to compute the critical temperature in the 2D Ising model.

Findings

Partition functions for finite lattices derived using graph theory and transfer matrix methods

Critical temperature estimation method demonstrated

Magnetization, susceptibility, and critical exponent calculated for infinite lattices

Abstract

The partition functions for two-dimensional nearest neighbour Ising model in a non-zero magnetic field have been derived for finite square lattices with the help of graph theoretical procedures, show-bit algorithm, enumeration of configurations and transfer matrix methods. A new recurrence relation valid for all lattice sizes is proposed. A novel method of computing the critical temperature has been demonstrated. The magnetization and susceptibility for infinite lattices in the presence of magnetic field is estimated. The critical exponent {\delta} pertaining to the magnetization has also been computed.