Topological Effects caused by the Fractal Substrate on the Nonequilibrium Critical Behavior of the Ising Magnet

TL;DR

This study investigates how the fractal structure of a substrate influences the nonequilibrium critical behavior of the Ising model, revealing topological effects like logarithmic oscillations and variable critical exponents through Monte Carlo simulations.

Contribution

It introduces the analysis of topological effects on critical dynamics of the Ising model on a fractal substrate, highlighting the role of discrete scale invariance and oscillatory behavior.

Findings

Logarithmic periodic oscillations in magnetization decay

Critical exponents depend on fractal segmentation step

Initial magnetization exponent nearly independent of fractal dimension

Abstract

The nonequilibrium critical dynamics of the Ising magnet on a fractal substrate, namely the Sierpinski carpet with Hausdorff dimension $d_H$ =1.7925, has been studied within the short-time regime by means of Monte Carlo simulations. The evolution of the physical observables was followed at criticality, after both annealing ordered spin configurations (ground state) and quenching disordered initial configurations (high temperature state), for three segmentation steps of the fractal. The topological effects become evident from the emergence of a logarithmic periodic oscillation superimposed to a power law in the decay of the magnetization and its logarithmic derivative and also from the dependence of the critical exponents on the segmentation step. These oscillations are discussed in the framework of the discrete scale invariance of the substrate and carefully characterized in order to determine the critical temperature of the second-order phase transition and the critical exponents corresponding to the short-time regime. The exponent $\theta $ of the initial increase in the magnetization was also obtained and the results suggest that it would be almost independent of the fractal dimension of the susbstrate, provided that $d_H$ is close enough to d=2.