Scaling of the equilibrium boundary of three-dimensional random-field Ising-model systems

Abstract

The onset of nonequilibrium behavior in three-dimensional random-field Ising-model (RFIM) systems (${\mathrm{Fe}}_{\mathrm{x}}$ ${\mathrm{Zn}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{F}}_2$; x=0.46,0.72) was studied via the capacitance method, using zero-field-cooling, field-cooling, and reverse-field-cooling techniques, in fields H≤100 kOe. Equilibrium was found to occur only above a boundary $T_{\mathrm{eq}\left(\mathrm{H}\right)}$, which lies slightly above the sharp phase transition $T_c$(H). Like $T_N$-$T_c$(H), $T_N$-$T_{\mathrm{eq}\left(\mathrm{H}\right)\mathrm{\alpha }{H}^{2/\phi }}$, after mean-field corrections; φ=1.40±0.05 is the random-field crossover exponent. Thus, the onset of nonequilibrium is tied to rf critical behavior. The scaling property of $T_{\mathrm{eq}\left(\mathrm{H}\right)}$ follows directly from Villain’s criterion for the breakdown of linear response in RFIM systems.