Inhomogeneities on all scales at a phase transition altered by disorder

TL;DR

This study investigates how quenched disorder affects phase transitions, revealing persistent inhomogeneities and the importance of averaging at quasicritical temperatures to accurately determine critical exponents.

Contribution

It demonstrates that averaging at quasicritical temperatures is essential for correct critical exponent estimation in disordered systems and highlights the growth of inhomogeneities with system size.

Findings

Inhomogeneities become more pronounced with increasing system size.

Averaging at quasicritical temperatures is necessary for accurate critical exponent measurement.

Different exponents describe fluctuations in disorder and thermodynamic ensembles.

Abstract

We have done a finite-size scaling study of a continuous phase transition altered by the quenched bond disorder, investigating systems at quasicritical temperatures of each disorder realization by using the equilibriumlike invaded cluster algorithm. Our results indicate that in order to access the thermal critical exponent $y_\tau$, it is necessary to average the free energy at quasicritical temperatures of each disorder configuration. Despite the thermal fluctuations on the scale of the system at the transition point, we find that spatial inhomogeneities form in the system and become more pronounced as the size of the system increases. This leads to different exponents describing rescaling of the fluctuations of observables in disorder and thermodynamic ensembles.