Binder Parameter of a Heisenberg Spin-Glass Model in Four Dimensions

TL;DR

This study investigates the phase transition behavior of a four-dimensional Heisenberg spin-glass model, revealing unusual Binder parameter behavior and suggesting a one-step RSB-like state below the transition temperature.

Contribution

It demonstrates that the Binder parameter does not cross for different sizes and proposes the occurrence of a one-step RSB-like state in the model.

Findings

Binder parameters do not cross for different sizes.

Strong anisotropy causes a steep negative dip in Binder parameters.

Possible one-step RSB-like state below the spin-glass transition temperature.

Abstract

We studied the phase transition of the $\pm J$ Heisenberg model with and without a random anisotropy on four dimensional lattice $L\times L\times L\times (L+1)$ $(L\leq 9)$. We showed that the Binder parameters $g(L,T)$'s for different sizes do not cross even when the anisotropy is present. On the contrary, when a strong anisotropy exists, $g(L,T)$ exhibits a steep negative dip near the spin-glass phase transition temperature $T_{\rm SG}$ similarly to the $p-$state infinite-range Potts glass model with $p \geq 3$, in which the one-step replica-symmetry-breaking (RSB) occurs. We speculated that a one-step RSB-like state occurs below $T_{\rm SG}$, which breaks the usual crossing behavior of $g(L,T)$.