Nonequilibrium relaxations within the ground-state manifold in the antiferromagnetic Ising model on a triangular lattice

Abstract

We present an extensive Monte Carlo simulation study on the nonequilibrium kinetics of triangular antiferromagnetic Ising model within the ground state ensemble which consists of sectors, each of which is characterized by a unique value of the string density p through a dimer covering method. Building upon our recent work [Phys. Rev. E 68, 066127 (2003)] where we considered the nonequilibrium relaxation observed within the dominant sector with p=2/3, we here focus on the nonequilibrium kinetics within the minor sectors with p<2/3. The initial configurations are chosen as those in which the strings are straight and evenly distributed. In the minor sectors, we observe a characteristic spatial anisotropy in both equilibrium and nonequilibrium spatial correlations. We observe emergence of a critical relaxation region (in the spatial and temporal domain) which grows as p deviates from p=2/3. Spatial anisotropy appears in the equilibrium spatial correlation with the characteristic length scale xi(e,V)(p) diverging with vanishing string density as xi(e,V)(p) approximately p(-2) along the vertical direction, while along the horizontal direction the spatial length scale diverges as xi(e,H) approximately p(-1). Analytic forms for the anisotropic equilibrium correlation functions are given. We also find that the spin autocorrelation function A(t) shows a simple scaling behavior A(t)=A(t/tau(A)(p)), where the time scale tau(A)(p) shows a power-law divergence with vanishing p as tau(A)(p) approximately p(-phi) with phi approximately or equal to 4. These features can be understood in terms of random walk nature of the fluctuations of the strings within the typical separation between neighboring strings.