Griffiths singularity in the two dimensional random bond disordered Ising ferromagnet

Abstract

For the two dimensional random bond disordered Ising ferromagnet, we measured bulk data of the magnetic susceptibility ($χ$) and correlation length ($ξ$) up to $ξ\simeq 536$, 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 $χ$ and $ξ$ increase continuously with the strength of disorder.