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

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.