Reentrant behavior of the spinodal curve in a nonequilibrium ferromagnet

The metastable behavior of a kinetic Ising-type ferromagnetic model system in which a generic type of microscopic disorder induces nonequilibrium steady states is studied by computer simulation and a mean-field approach. We pay attention, in particular, to the spinodal curve or intrinsic coercive field that separates the metastable region from the unstable one. We find that, under strong nonequilibrium conditions, this exhibits reentrant behavior as a function of temperature. That is, metastability does not happen in this regime for both low and high temperatures, but instead emerges for intermediate temperature, as a consequence of the nonlinear interplay between thermal and nonequilibrium fluctuations. We argue that this behavior, which is in contrast with equilibrium phenomenology and could occur in actual impure specimens, might be related to the presence of an effective multiplicative noise in the system.

Figure 1

Two examples of spin domains, each following from a different lattice partition $\mathbb{P}\left(\Lambda \right)$; see the main text. The spins that do not belong to the domain are in black, surface spins are gray, and the spins forming the domain interior are empty.

Figure 2

Variation with $p$ of the critical temperature for the nonequilibrium ferromagnetic system in the first-order mean-field approximation. The solid line in the inset stands for the locally-stable steady magnetization as a function of temperature (in units of the equilibrium critical value) for $h=0$ and, from top to bottom, $p=0$, $0.001$, $0.005$, and $0.01$. The symbols in the inset are Monte Carlo results for a $53\times 53$ lattice.

Figure 3

$h^{*}(T,p)$, as a function of $T$ for, from top to bottom, $p=0$, 0.01, 0.02, 0.03, 0.031, 0.032, 0.035, 0.04, 0.05, and 0.1. The qualitative change of behavior in the low temperature region occurs for $p∊(0.031,0.032)$. Inset: The two locally-stable steady magnetization branches as a function of $h$ for $T=0.7T_c\left(0\right)$ and $p=0.005$. The solid (dashed) line represents stable (metastable) states. The dotted-dashed line signals the discontinuous transition, at $h=h^{*}(T,p)$, where metastable states disappear.

Figure 4

Monte Carlo results for $h^{*}(T,p)$ as a function of $T$ for $L=53$ and, from top to bottom, $p=0$, 0.01, 0.03, 0.0305, 0.0320, 0.0350, 0.04, and $0.05$. Notice the change of asymptotic behavior in the low temperature limit for $p∊(0.03,0.0305)$. Inset: The probability of the metastable state, as defined in the main text, as a function of $h<0$ for $L=53$, $T=0.7T_c\left(0\right)$, and $p=0$. Data here correspond to an average over 500 independent demagnetization experiments for each value of $h$. Error bars are smaller than the symbol sizes.