Evidence of a one-step replica symmetry breaking in a three-dimensional Potts glass model

We study a seven-state Potts glass model in three dimensions with first-, second-, and third-nearest-neighbor interactions with a bimodal distribution of couplings by Monte Carlo simulations. Our results show the existence of a spin-glass transition at a finite temperature $T_c$, a discontinuous jump of an order parameter at $T_c$ without latent heat, and a nontrivial structure in the order parameter distribution below $T_c$. They are compatible with one-step replica symmetry breaking.

Figure 1

Temperature dependence of the dimensionless correlation length ${\xi }_L/L$. Inset shows enlarged view around the transition temperature.

Figure 2

Scaling plot of the finite-size correlation length ratio ${\xi }_L/L$ according to Eq. (8) using $T_c/J=0.421,\nu =0.68,a=1$, and $\omega =3$. Inset shows magnified view.

Figure 3

Overlap distribution function of a Potts glass model in three dimensions (a) for various temperatures with $L=9$ and (b) for different sizes at $T/J=0.2970$ below $T_c$.

Figure 4

Temperature dependence of the Binder parameter $g_4$ of a Potts glass model in three dimensions.

Figure 5

Temperature dependence of (a) energy density and (b) specific heat.