Strong universality class in disordered systems

TL;DR

This paper investigates the impact of disorder on magnetic systems using Monte Carlo simulations, revealing a strong universality class where certain critical exponents and fractal dimensions remain invariant despite disorder.

Contribution

It introduces the concept of a strong universality class in disordered magnetic systems, identifying invariant critical exponents and fractal dimensions across different disorder levels.

Findings

Disorder alters critical exponents, leading to different universality classes.

A subgroup of critical exponents and fractal dimensions remains invariant with disorder.

Monte Carlo simulations validate analytical predictions about the universality class.

Abstract

Disordered systems are very rich laboratories for exploring complex systems. In particular, disordered magnetic systems have been extremely important in the last five decades for understanding a wide range of phenomena. In this work, we use the Edwards-Anderson Hamiltonian to obtain the thermodynamic properties of disordered magnetic systems. In this way, we conduct a systematic investigation of magnetization, correlation functions, order parameter, and fractal dimensions, in function of disorder. In this context, the autocorrelation function for order--parameter fluctuations, introduced by Fisher ( Journal of Mathematical Physics 5, 944322 (1964)), provides an important mathematical framework for understanding the second-order phase transition at equilibrium. However, his analysis is restricted to a Euclidean space of dimension $d$, and an exponent $\eta$ is introduced to correct the spatial behavior of the correlation function at $T=T_c$. In recent work, Lima et al ( Phys. Rev. E 110, L062107 (2024)) demonstrated that at $T_c$ a fractal analysis is necessary for a complete description of the correlation function. We use Monte Carlo simulations to validate analytical results and to show how disorder alters critical exponents , giving rise to different universality classes. On the other hand, there is a subgroup of critical exponents and fractal dimensions that are invariant with disorder. This subgroup heralds a strong universality class.