Anomalous Size Dependence of Relaxation Time in the Fuzzy Spin Model: Mechanism of Slow Relaxation

Abstract

Slow relaxation phenomena are studied in the Fuzzy Spin Model which is a random Ising ferromagnetic model with random spin length. The model is found to have many metastable states, which cause an anomalous relaxation. Distribution of the relaxation time to the ferromagnetic equilibrium state is investigated by the Monte Carlo method after quenching rapidly the system (the two-dimensional square lattice) from infinite temperature to temperatures below the critical point. Up to a certain size, linear dimension L'20, the mean relaxation time increases exponentially with the size Las rcx:exp(aL)(a >0), which is understood to be due to a relaxation based on overturns of strongly coupled domains. Above L'20, a different relaxation mechanism sets in, which shows a weaker size dependence. Mechanism of the size dependences of the relaxation is discussed in the viewpoint of distribution of the domains.