Critical behavior of the Ising model under strong shear: The conserved case

Abstract

The non-equilibrium phase transitions of the two-dimensional magnetization-conserved Ising model under the action of an external shear field is investigated. This field, that simulates a convective velocity profile with shear rate γ̇, introduces anisotropic effects and forces the system to evolve into non equilibrium states. By employing the short-time dynamics (STD) methodology, it was possible to detect first- and second-order phase transitions, and in this last case the critical exponent were calculated. As a function of the absolute magnetization |M| the system exhibits phase transitions of different order. On the one hand, If |M|=0, the model undergoes a second-order phase transition. The estimated critical temperature Tc depends on γ̇ and two regimes can be distinguished: a power-law regime for low γ̇′s, and a saturation regime at larger values of it. For the investigated shear field interval, the estimated values of the anisotropic critical exponents suggest that the critical behavior is on a crossover between the Ising and mean-field critical behaviors, respectively. On the other hand if |M|>0, the model exhibits for each γ̇ first-order phase transitions, ending in a critical point at |M|=0.