Off-equilibrium scaling behaviors driven by time-dependent external fields in three-dimensional O(N) vector models
Year: 2016
Type: article
Abstract: We consider the dynamical off-equilibrium behavior of the three-dimensional $\mathrm{O}(N)$ vector model in the presence of a slowly varying time-dependent spatially uniform magnetic field $\mathbit{H}(t)=h(t)\phantom{\rule{0.16em}{0ex}}\mathbit{e}$, where $\mathbit{e}$ is an $N$-dimensional constant unit vector, $h(t)=t/{t}_{s}$, and ${t}_{s}$ is a time scale, at fixed temperature $T\ensuremath{\le}{T}_{c}$, where ${T}_{c}$ corresponds to the continuous order-disorder transition. The dynamic evolutions start from equilibrium configurations at ${h}_{i}<0$, correspondingly ${t}_{i}<0$, and end at time ${t}_{f}>0$ with $h({t}_{f})>0$, or vice versa. We show that the magnetization displays an off-equilibrium scaling behavior close to the transition line $\mathbit{H}(t)=0$. It arises from the interplay among the time $t$, the time scale ${t}_{s}$, and the finite size $L$. The scaling behavior can be parametrized in terms of the scaling variables ${t}_{s}^{\ensuremath{\kappa}}/L$ and $t/{t}_{s}^{{\ensuremath{\kappa}}_{t}}$, where $\ensuremath{\kappa}>0$ and ${\ensuremath{\kappa}}_{t}>0$ are appropriate universal exponents, which differ at the critical point and for $T<{T}_{c}$. In the latter case, $\ensuremath{\kappa}$ and ${\ensuremath{\kappa}}_{t}$ 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 ${T}_{c}$. 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.
Source: Physical review. E
Authors: Andrea Pelissetto, Ettore Vicari
Language: Latvian
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2329592571