Phase diagram of the dilute Ising spin glass in general spatial dimension.

Abstract

We use high-temperature and low-concentration series to treat the dilute spin glass within a model with nearest-neighbor interactions which randomly assume the values +J, 0, -J with probabilities p/2, 1-p, p/2, respectively. Using the Harris no-free-end diagrams scheme in general spatial dimension, we obtained 15th-order series for ${\mathrm{\ensuremath{\chi}}}^{\mathrm{EA}}$ as a function of temperature for arbitrary dilution, 14th-order series for ${\mathrm{\ensuremath{\chi}}}^{\mathrm{EA}}$ as a function of dilution for selected temperatures, and 11th-order series for two higher derivatives of ${\mathrm{\ensuremath{\chi}}}^{\mathrm{EA}}$ with respect to the ordering field, where ${\mathrm{\ensuremath{\chi}}}^{\mathrm{EA}}$ is the Edwards-Anderson spin-glass susceptibility. Analysis of these series yields values of ${\mathit{T}}_{\mathrm{SG}}$(p), the critical temperature as a function of the dilution p or the analogous critical concentration ${\mathit{p}}_{\mathrm{SG}}$(T). Thus we determine a critical line, separating the spin-glass phase from the paramagnetic phase in the T-p plane. We find values of the critical exponent \ensuremath{\gamma} and universal amplitude ratios along the critical line. Universal amplitude ratios and dominant exponents along the critical line are identical to those of the pure spin glass for a wide range of dilution, indicating the same critical behavior as that of the pure spin glass.