Static and dynamic magnetic response of spin-glass models with short-range interactions

Abstract

The static and dynamic magnetic response of the two-dimensional Edwards-Anderson model with a nearest-neighbor Gaussian exchange distribution is investigated by Monte Carlo simulation. A plateau in the equilibrium (slowly field cooled) susceptibility $\frac{M_{\mathrm{eq}}}{H}$ is found, which diverges for small fields with a power law $\frac{M_{\mathrm{eq}}}{H}\propto H^{\frac{1}{\Delta }}$, $\Delta =3.5\mathrm{}\pm 0.5$. The boundary of the plateau $H_c^{\mathrm{eq}}\mathrm{}\left(T\right)\mathrm{}$ tends to zero temperature as $H_c^{\mathrm{eq}}\mathrm{}\left(T\right)\mathrm{}\propto T^{\Delta }$, consistent with a scaling description appropriate for a static phase transition at $T=0\mathrm{}$, and the associate scaling function is estimated. Surprisingly the data also are consistent with a scaling representation with nonzero freezing temperatures $T_f$, in striking similarity to experimental data, but $T_f=0\mathrm{}$ is shown to be the correct choice. The zero-field-cooled susceptibility starts to differ from $\frac{M_{\mathrm{eq}}}{H}$ below a certain critical field $H_c\mathrm{}\left(t\right)\mathrm{}$, $t$ being the time scale over which the field is applied. In the $H-T$ plane $H_c\mathrm{}\left(t\right)\mathrm{}$ extrapolates to a time-dependent freezing temperature $T_c\mathrm{}\left(t\right)\mathrm{}$, and closely resembles the de Almeida—Thouless line. A tentative interpretation of these findings is attempted by combining scaling considerations with the reorientation of correlated clusters which have the size of the correlation length describing Edwards-Anderson order. The reduction of the free-energy barriers due to the magnetic field is treated in analogy with the interface free-energy reduction of ferromagnets in random fields.