Metastable Behavior in Relaxation Process of XY Fuzzy Spin Model

Abstract

In the previous papers 0 • 2 > we have shown that the relaxation time in the Ising-type fuzzy spin model(IFSM) becomes anomalously longer than that of the standard uniform Ising spin model, due to the existence of the metastable states generated by pinning of domain walls, which comes from the topological disorder of the model. 3 > Namely the metastable states consist of the domain-like structures centered at large spins in IFSM, which are long-lived since they are separated by boundaries (walls) formed with small spins. In IFSM the order parameter of the model is of the Ising one which has a discrete twofold symmetry, namely a Zz symmetry. Thus the topological defect of the model is the domain wall. 3 > In the pure system the domain wall costs the same energy at any places while in the random system such as IFSM it costs smaller energy at places with small spins. This inhomogeneity causes the pinning of the domain walls. Contrary to the spin glasses where the frustration is essential to the degenerated metastable states, we insist that the randomness is important as well as the frustration to the study of the metastable states and anoma­ lous slow relaxation. In this paper we wish to demonstrate that even in the continuous spin system the metastable states are generated by pinning of the topological defect of the model, namely a vortex, in random systems, which will result in anomalous relaxation phenomena. In the XY model the pinned vortex alignment of spins is found to play the role of long-lived, metastable spin configurations before reaching the equilibrium state of the system. When being quenched to 0 K, the average energy of metastable states per spin is 0.976 times the ground state energy, almost independent of system size in the large limit. Number of the quenched vorticies is proportional to the area of the lattice, which means sizes of the vortices are independent of the lattice size. The average size of the vortices is found to be about 10 lattice units, which is consistent with our estimation based on vortex formation energy. Average barrier heights among the metastable states are estimated to be 0.06 l by using magnetic field to be required for dissolving the vortices. It also means that the vortex pinning effect is significant only in the region, T s 0.06]. In the relaxation process at finite temper