Finite-Size Scaling and Damage Spreading in Ising Systems with Multispin Interactions

TL;DR

This paper studies two-dimensional Ising models with three- and four-body interactions, using a new finite-size algorithm to distinguish the nature of phase transitions and examining damage spreading phenomena.

Contribution

It applies a novel finite-size algorithm to differentiate first-order and continuous transitions in multispin Ising systems and explores damage spreading dynamics at critical points.

Findings

First-order transition identified in four-body interaction case.

Continuous transition observed in three-body interaction case.

Damage spreading occurs at a critical point, but does not conclusively determine transition order.

Abstract

We investigate two-dimensional Ising systems with multisping interactions of three- (m=3) and four-body terms (m=4). The application of a new type of finite-size algorithm of de Oliveira allow us to clearly distinguish a first-order transition (in the m=4 case) from a continuous one (in the m=3 one). We also study the damage spreading in these systems. In this study, a dynamical phenomenon is observed to occur at a critical point separating a chaotic phase from a frozen one. However, the width of the interval where this transition happens does not yield a conclusive evidence about the order of the phase transition.