New critical behaviour of the three-dimensional Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions

TL;DR

This paper investigates the critical and multicritical behavior of a 3D Ising model with complex interactions, revealing a new universality class and providing detailed critical exponent estimates using advanced approximation methods.

Contribution

It introduces novel analysis of the 3D Ising model with multiple interactions, identifying a new universality class and calculating critical exponents with cluster variation methods.

Findings

Identification of a new universality class for the phase transition.

Calculation of critical exponents at critical end points.

Estimate of the crossover exponent.

Abstract

The critical and multicritical behavior of the simple cubic Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions is studied using the cube and star-cube approximations of the cluster variation method and the recently proposed cluster variation--Pad\'e approximant method. Particular attention is paid to the line of critical end points of the ferromagnetic-paramagnetic phase transition: its (multi)critical exponents are calculated, and their values suggest that the transition belongs to a novel universality class. A rough estimate of the crossover exponent is also given.