Noise-driven dynamic phase transition in a one-dimensional Ising-like model

The dynamical evolution of a recently introduced one-dimensional model [S. Biswas and P. Sen, Phys. Rev. E 80, 027101 (2009)] (henceforth, referred to as model I), has been made stochastic by introducing a parameter beta such that beta=0 corresponds to the Ising model and beta>infinity to the original model I. The equilibrium behavior for any value of beta is identical: a homogeneous state. We argue, from the behavior of the dynamical exponent z, that for any beta not equal 0, the system belongs to the dynamical class of model I indicating a dynamic phase transition at beta=0. On the other hand, the persistence probabilities in a system of L spins saturate at a value P-sat(beta, L)=(beta/L)(alpha)f(beta), where alpha remains constant for all beta not equal 0 supporting the existence of the dynamic phase transition at beta=0. The scaling function f(beta) shows a crossover behavior with f(beta)=constant for beta << 1 and f(beta)proportional to beta(-alpha) for beta >> 1.