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تسجيل مستخدم جديدde Almeida-Thouless instability in short-range Ising spin-glasses
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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 $dge 6$. 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 $dge 6$. 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 $d=5$.
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