Virtual walks in the Ising model: Finite-time scaling.

Abstract

The dynamics of the spins in the Ising model are analyzed using a virtual walk scenario. The system is quenched from a very high temperature to a lower one using the Glauber scheme in one and two dimensions. A walk is associated with each spin which evolves according to the current state of the spin. The probability distribution of the displacement of the walker is calculated, which shows a distinct change as the temperature is increased. The average displacement as a function of time shows a nonequilibrium region stretched over a much longer time interval compared to the bulk magnetization. Nevertheless, one can still detect a time-dependent estimate of the critical point determined by two different methods. In addition, we introduce a virtual walk generated from the local energy of individual spins. Finite-time scaling of the different quantities estimated in two dimensions shows excellent consistency with the values of the known critical exponents.