Transformations of mixed spin-class Ising systems

TL;DR

This paper demonstrates how to transform mixed spin-class Ising systems into equivalent forms, enabling analysis across different spin-variable types without altering the overall probability distribution.

Contribution

It introduces a method to convert between various mixed spin-class Ising models using simple transformations, unifying different spin-variable representations.

Findings

Transformations preserve the probability distribution of system states.

All mixed spin-class Ising models are equivalent under suitable variable transformations.

The method applies to any combination of binary real-valued spin-classes.

Abstract

In the many fields in which the Ising model is applied nowadays, the spin variables are often assumed to be of spin-class $\{-1,1\}$ or $\{0,1\}$, even though for any mix of binary real valued spin-classes a proper Ising model distribution exists. Here we show that in their basis all these spin-classes are the same, as a simple expressions exist that allow us to transform the variables from one particular mix of spin-classes to any other combination, without changing the probabilities for the system states as a whole.