Super-Potts glass: A disordered model for glass-forming liquids

We introduce a disordered system, the super-Potts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take $M$ values and are coupled via pairwise interactions. Its exact solution on a completely connected lattice demonstrates that, for large enough $M$, it belongs to the class of mean-field systems solved by a one-step replica symmetry breaking ansatz. Numerical simulations by the parallel tempering technique show that in three dimensions it displays a phenomenological behavior similar to the one of glass-forming liquids. The super-Potts glass is therefore a disordered model allowing one to perform extensive and detailed studies of the random first-order transition in finite dimensions. We also discuss its behavior for small values of $M$, which is similar to the one of spin glasses in a field.

Figure 1

Two-time correlation function for systems with $M=30$ and $L=8$ (main panel, inverse temperature $\beta$ equally spaced in $[0.28,0.85]$, from left to right) and with $L=12$ $M=4$ (inset, $\beta$ equally spaced in $[0.76,1.09]$, from left to right). Note that the characteristic two-step relaxation emerges on top of the asymptotic value $C\left(\infty \right)=q_0>0$.

Figure 2

Four-point susceptibility for a system with $L=8,M=30$ (main panel) and with $L=12,M=4$ (inset). Temperatures as in Fig. 1.

Figure 3

$P\left(q\right)$ for a system with $L=10,M=20$. $\beta$ equally spaced in $[0.55,1.3]$ (from left to right).