Spin glass phase in the four-state three-dimensional Potts model

We perform numerical simulations, including parallel tempering, a four-state Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the critical temperature and the value of the critical exponents. Nevertheless, the extrapolation to infinite volume is hampered by strong scaling corrections. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the “random permutation” Potts glass.

Figure 1

(Color online) A thermalization test. We show the behavior of the time-dependent spin glass correlation length as a function of Monte Carlo time. We have averaged the correlation length using a logarithmic binning procedure. We show data for the lowest temperature simulated for each size.

Figure 2

(Color online) The spin glass correlation length divided by $L$ as a function of $\beta$ for $L=4$, 6, 8, and 16. In the inset we magnify the crossing between the $L=8$ and $L=16$ curves.

Figure 3

(Color online) We show the behavior of the magnetic susceptibility, ${\chi }_M$, versus the inverse temperature. Notice that this susceptibility saturates in the critical region. In the inset we have plotted the average of the modulus of the magnetization, $\overline{⟨|\mathit{m}|⟩}$, against the temperature: this observable behaves as $1/\sqrt{N}$ which clearly signals a paramagnetic behavior.