de Almeida-Thouless instability in short-range Ising spin-glasses

Abstract

We use high temperature series expansions to study the $\pm J$ Ising spin-glass in a magnetic field in $d$-dimensional hypercubic lattices for $d=5,6,7$ and $8$, and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable $w={\tanh }^{2}J/T$ for arbitrary values of $u={\tanh }^{2}h/T$ complete to order $w^{10}$. We find that the scaling dimension $\Delta$ associated with the ordering-field $h^2$ equals $2$ in the SK model and for $d\ge 6$. However, in agreement with the work of Fisher and Sompolinsky, there is a violation of scaling in a finite field, leading to an anomalous $h$-$T$ dependence of the Almeida-Thouless (AT) line in high dimensions, while scaling is restored as $d\to 6$. Within the convergence of our series analysis, we present evidence supporting an AT line in $d\ge 6$. In $d=5$, the exponents $\gamma$ and $\Delta$ are substantially larger than mean-field values, but we do not see clear evidence for the AT line in $d=5$.

5 pages and 5 figures. Series coefficients in Supplementary Materials

References in corpus (4)

• Diluted one-dimensional spin glasses with power law decaying interactions
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Spin glasses in a field: Three and four dimensions as seen from one space dimension
• The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority

Cited by in corpus (6)

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• Multicritical point on the de Almeida-Thouless line in spin glasses in $d>6$ dimensions
• Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field
• Efficient generation of series expansions for $\pm J$ Ising spin-glasses in a classical or a quantum (transverse) field
• Evidence of de Almeida-Thouless line below six dimensions