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

Abstract

The dynamical evolution of a recently introduced one dimensional model in \cite{biswas-sen} (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 $\beta \to \infty$ to the original model I. The equilibrium behaviour for any value of $\beta$ is identical: a homogeneous state. We argue, from the behaviour of the dynamical exponent $z$,that for any $\beta \ne 0$, 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 $\beta \ne 0$ supporting the existence of the dynamic phase transition at $\beta =0$. The scaling function $f(\beta )$ shows a crossover behaviour with $f(\beta )=\mathrm{constant}$ for $\beta <<1$ and $f(\beta )\propto {\beta }^{-\alpha }$ for $\beta >>1$.

4 pages, 5 figures, accepted version in Physical Review E

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