Hysteretic scaling and dynamical phase transition of three-dimension X-Y Model

Abstract

We have studied in this paper,by performing the Monte Carlo numerical simulation,both the hysteretic scaling and the dynamical phase transition of a three-dimen sional,(3D) classical X-Y model driven by an sinusoidally oscillating external m agnetic field.A scaling formula has been worked out which relates the hysteresis loop area with the amplitude h0 and frequency ω of the external fie ld as wel l as the reduced temperature T/Tc of the system in the form:Area～hα0ωβ(1-T/Tc)γ.The best-fit expo nents are α=0.57,β=0.34 and γ=0.9.The 3D X- Y model also characterizes a distinctive discrepancy in dynamical transition fea ture after short and long term evolution of magnetization,respectively.Our simul ation disclosed that the short-term evolution of magnetization (period number≤1 0) attains the symmetry-breaking of system with a nonzero dynamical order parame ter (Q≠0) at a either critical amplitude h0c or frequency ωc.The symme try-breaking in short term,however,evolves steadily into a symmetric disorder st ate (Q=0) after a longer term relaxation of system.The specific relaxation times at which the Q value becomes zero from nonzero increase evidently as the temper ature of system drops.