2015/12/31 by Andrea Pelissetto, Ettore Vicari · 2 citations
Physics and Astronomy · #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.93.032141
published as Phys. Rev. E 93, 032141 (2016) · 16 pages, extended text and refs
arxiv created 2016/03/07 · arxiv updated 2016/03/30
We consider the dynamical off-equilibrium behavior of the three-dimensional O(N) vector model in the presence of a slowly-varying time-dependent spatially-uniform magnetic field \bm H(t) = h(t) \bm e, where \bm e is a N-dimensional constant unit vector, h(t)=t/ts, and ts is a time scale, at fixed temperature T≤ Tc, where Tc corresponds to the continuous order-disorder transition. The dynamic evolutions start from equilibrium configurations at hi < 0, correspondingly ti < 0, and end at time tf > 0 with h(tf) > 0, or vice versa. We show that the magnetization displays an off-equilibrium scaling behavior close to the transition line \bm H(t)=0. It arises from the interplay among the time t, the time scale ts, and the finite size L. The scaling behavior can be parametrized in terms of the scaling variables tsκ/L and t/tsκt, where κ>0 and κt > 0 are appropriate universal exponents, which differ at the critical point and for T < Tc. In the latter case, κ and κt also depend on the shape of the lattice and on the boundary conditions. We present numerical results for the Heisenberg (N=3) model under a purely relaxational dynamics. They confirm the predicted off-equilibrium scaling behaviors at and below Tc. We also discuss hysteresis phenomena in round-trip protocols for the time dependence of the external field. We define a scaling function for the hysteresis loop area of the magnetization that can be used to quantify how far the system is from equilibrium.