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 $\frac{{M}_{\mathrm{eq}}}{H}\ensuremath{\propto}{H}^{\frac{1}{\ensuremath{\Delta}}}$, $\ensuremath{\Delta}=3.5\ifmmode\pm\else\textpm\fi{}0.5$. The boundary of the plateau ${H}_{c}^{\mathrm{eq}}(T)$ tends to zero temperature as ${H}_{c}^{\mathrm{eq}}(T)\ensuremath{\propto}{T}^{\ensuremath{\Delta}}$, consistent with a scaling description appropriate for a static phase transition at $T=0$, 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 ${T}_{f}=0$ 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 ${H}_{c}(t)$, $t$ being the time scale over which the field is applied. In the $H\ensuremath{-}T$ plane ${H}_{c}(t)$ extrapolates to a time-dependent freezing temperature ${T}_{c}(t)$, 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.