1-d Ising model using Kronecker sum and Kronecker product

TL;DR

This paper introduces a simplified matrix-based formulation for the 1-D Ising model using Kronecker sum and product, making calculations more intuitive and accessible for various configurations.

Contribution

It presents a novel approach that represents microstates as diagonal matrices, simplifying calculations in the 1-D Ising model with different boundary conditions and magnetic fields.

Findings

Simplifies Ising model calculations using matrix operations.

Addresses open-chain and closed-chain configurations.

Provides a pedagogical tool for students and researchers.

Abstract

Calculations in Ising model can be cumbersome and non-intuitive. Here we provide a formulation that addresses these issues for 1-D scenario. We represent the microstates of spin interactions as a diagonal matrix. This is done using two operations: Kronecker sum and Kronecker product. The calculations thus become simple matter of manipulating diagonal matrices. We address the following problems in this work: spins in the magnetic field, open-chain 1-D Ising model, closed-chain 1-D Ising model, 1-D Ising model in an external magnetic field. We believe that this representation will help provide students as well as experts with a simple yet powerful technique to carry out calculations in this model.