Fractal signatures of strong universality in the disordered Ising model

Henrique A Lima; Kaue Hermann; Ismael S. S. Carrasco; Jairo R. L. de Almeida; Fernando A. Oliveira

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arXiv · 2605.15441

Fractal signatures of strong universality in the disordered Ising model

Henrique A Lima·Kaue Hermann·Ismael S. S. Carrasco·Jairo R. L. de Almeida·Fernando A. Oliveira

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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.

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Henrique A Lima, Kaue Hermann, Ismael S. S. Carrasco, Jairo R. L. de Almeida, Fernando A. Oliveira. 2026-05-14. Fractal signatures of strong universality in the disordered Ising model. https://arxiv.org/abs/2605.15441

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