Griffiths singularity in the two dimensional random bond disordered Ising ferromagnet

TL;DR

This study uses advanced Monte Carlo simulations to investigate the critical behavior of a two-dimensional disordered Ising ferromagnet, finding no evidence of Griffiths singularity and revealing disorder-dependent critical exponents.

Contribution

It introduces a novel finite size scaling Monte Carlo method to accurately measure critical behavior in disordered systems, challenging previous claims of Griffiths singularity.

Findings

Critical exponents increase with disorder strength

No Griffiths singularity observed in deep scaling region

Power-law critical behavior with a single singular point

Abstract

For the two dimensional random bond disordered Ising ferromagnet, we measured bulk data of the magnetic susceptibility ($\chi$) and correlation length ($\xi$) up to $\xi \simeq 536$, with the use of a novel finite size scaling Monte Carlo technique. Our data are exclusively consistent with normal power-law critical behaviors with only one singular point at criticality, disproving the existence of Griffiths singularity even in an extremely deep scaling region. The critical exponents of $\chi$ and $\xi$ increase continuously with the strength of disorder.