Scaling and finte-size-scaling in the two dimensional random-coupling Ising ferromagnet

TL;DR

This paper uses Monte Carlo simulations to confirm finite size scaling in the 2D random-coupled Ising ferromagnet and explores how the universal FSS function varies with disorder strength, supporting the weak universality scenario.

Contribution

It demonstrates finite size scaling in the 2D random Ising model and shows the dependence of the universal FSS function on disorder strength, providing insights into critical behavior under randomness.

Findings

Finite size scaling holds in the 2D random Ising ferromagnet.

The universal FSS function depends on the disorder strength.

Data supports the weak universality scenario.

Abstract

It is shown by Monte Carlo method that the finite size scaling (FSS) holds in the two dimensional random-coupled Ising ferromagnet. It is also demonstrated that the form of universal FSS function constructed via novel FSS scheme depends on the strength of the random coupling for strongly disordered cases. Monte Carlo measurements of thermodynamic (infinite volume limit) data of the correlation length ($\xi$) up to $\xi \simeq 200$ along with measurements of the fourth order cumulant ratio (Binder's ratio) at criticality are reported and analyzed in view of two competing scenarios. It is demonstrated that the data are almost exclusively consistent with the scenario of weak universality.