Two temperature Ising Model

TL;DR

This paper introduces a two-temperature Ising model to study superstatistic critical phenomena, developing Monte Carlo methods to analyze its phase diagram and critical behavior, revealing a non-trivial critical line with Ising universality.

Contribution

The paper presents a novel two-temperature Ising model and provides analytical and numerical analysis of its phase diagram and critical exponents, extending understanding of superstatistic critical phenomena.

Findings

Existence of a non-trivial critical line separating phases

Critical exponents match the Ising universality class

Analytic equation for the critical line proposed

Abstract

We introduce a two-temperature Ising model as a prototype of superstatistic critical phenomena. The model is described by two temperatures ($T_1,T_2$) in zero magnetic field. To predict the phase diagram and numerically estimate the exponents, we develop Metropolis and Swendsen-Wang Monte Carlo method. We observe that there is a non-trivial critical line, separating ordered and disordered phases. We propose an analytic equation for the critical line in the phase diagram. Our numerical estimation of the critical exponents illustrates that all points on the critical line belong to the ordinary Ising universality class.