Static and Dynamic Critical Magnetic Fields in Ising Spin-Glasses

Abstract

By Monte Carlo simulations it is shown that the magnetization $M(T, H)$ of the two-dimensional nearest-neighbor Edwards-Anderson model is proportional to $H^{1-x}$, essentially independent of temperature $T$, for fields $H<\mathrm{}{H_c}^{\mathrm{eq}}\mathrm{}\left(T\right)\mathrm{}$, with ${H_c}^{\mathrm{eq}}\mathrm{}\left(T\right)\mathrm{}\propto T^{\frac{1}{x}}$, the exponent being $x\approx 0.28\pm 0.06$. Irreversible behavior on a time scale $t$ sets in for a field $H_c\mathrm{}\left(t\right)\mathrm{}$ where $\frac{H_c\mathrm{}\left(t\right)\mathrm{}}{T_f\mathrm{}\left(t\right)\mathrm{}}$ nearly follows the De Almeida-Thouless line, although no static nonzero freezing temperature $T_f$ exists. Consequences for the interpretation of related experimental work are discussed.