Emergence of the 3D diluted Ising model universality class in a mixture of two magnets

TL;DR

This study shows that structural disorder alone, without non-magnetic impurities, can lead to the emergence of the 3D diluted Ising universality class in a mixture of two different Ising magnets, confirmed by Monte Carlo and renormalization group analyses.

Contribution

It demonstrates that disorder in spin arrangement, not non-magnetic components, causes the universality class change in 3D Ising models, supported by simulations and theoretical calculations.

Findings

Emergence of 3D diluted Ising universality class due to structural disorder.

Critical exponents match those of site-diluted 3D Ising model.

Effective critical behavior depends on spin length and concentration parameters.

Abstract

Usually, the impact of structural disorder on the magnetic phase transition in the 3D Ising model is analyzed within the framework of quenched dilution by a non-magnetic component, where some lattice sites are occupied by Ising spins, while others are non-magnetic. This kind of quenched dilution, according to the Harris criterion, leads to a change in the critical exponents that govern the asymptotics in the vicinity of the phase transition point. However, the inherent reason for the emergence of a new, random Ising model universality class is not the presence of a non-magnetic component but the disorder in structure of spin arrangement. To demonstrate this fact, in this paper, we set up extensive Monte Carlo simulations of a random mixture of two Ising-like magnets that differ in spin length $s$ and concentration $c$. In doing so, we analyze the effect of structural disorder \textit{per se} without appealing to the presence of a non-magnetic component. We support our numerical simulations with renormalization group calculations. Our results demonstrate the emergence of the 3D randomly diluted Ising model universality class in a random mixture of two Ising magnets. While the asymptotic critical exponents coincide with those known for the site-diluted 3D Ising model, the effective critical behavior is triggered by parameters $s$ and $c$. The impact of their interplay is a subject of detailed analysis.