Universality Class of the Nonequilibrium Phase Transition in Two-Dimensional Ising Ferromagnet Driven by Propagating Magnetic Field Wave

Abstract

The finite size analysis of the nonequilibrium phase transition, in two dimensional Ising ferromagnet driven by plane propagating magneticwave, is studied by Monte Carlo simulation. It is observed that the system undergoes a nonequilibrium dynamicphase transition from a high temperature dynamically symmetric ({\it propagating}) phase to a low temperature dynamically symmetry-broken ({\it pinned}) phase as the system is cooled below the transition temperature. This transition temperature is determined precisely by studying the fourth order Binder Cumulant of the dynamic order parameter as a function of temperature for different system sizes ($L$). From the finite size analysis of dynamic order parameter ($Q_L \sim L^{-{{\beta} \over {\nu}}}$) and the dynamic susceptibility ($\chi^{Q}_{L} \sim L^{{\gamma} \over {\nu}}$), we have estimated the critical exponents $\beta/\nu=0.146\pm0.025$ and $\gamma/\nu=1.869\pm0.135$ (measured from the data read at the critical temperature obtained from Binder cumulant), and $\gamma/\nu=1.746\pm0.017$ (measured from the peak positions of dynamic susceptibility). Our results indicate that such driven Ising ferromagnet belongs to the same universality class of the two-dimensional equilibrium Ising ferromagnet (where $\beta/\nu=1/8$ and $\gamma/\nu=7/4$), within the limits of statistical errors.