Fractal signatures of strong universality in the disordered Ising model
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 η is introduced to correct the spatial behavior of the correlation function at T=Tc. In recent work, Lima et al ( Phys. Rev. E 110, L062107 (2024)) demonstrated that at Tc 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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BibTeX
@misc{lima2026fractal,
title = {{Fractal signatures of strong universality in the disordered Ising model}},
author = {Henrique A Lima and Kaue Hermann and Ismael S. S. Carrasco and Jairo R. L. de Almeida and Fernando A. Oliveira},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.15441},
eprint = {2605.15441},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15441},
}
RIS
TY - UNPB
TI - Fractal signatures of strong universality in the disordered Ising model
AU - Henrique A Lima
AU - Kaue Hermann
AU - Ismael S. S. Carrasco
AU - Jairo R. L. de Almeida
AU - Fernando A. Oliveira
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2605.15441
UR - https://arxiv.org/abs/2605.15441
AB - 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 η 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.
ER -