Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange : A Monte Carlo study

Abstract

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor ±Ĵ-interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (T/Ĵ ≥ 0.6). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, q(t) ∝ exp[‒(t/τ) y(T) ], while a power law prefactor cannot be distinguished. The Kohlrausch exponent y(T) decreases from y ≈ 0.64 at T/Ĵ = 1.1 to y ≈ 0.37 at T/Ĵ = 0.6 however. The relaxation time τ is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, lnτ ∝ T‒ σ but the exponent σ that can be extracted (σ ≈ 2.5) still differs significantly from the theoretical value, σ = 3. Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass.