de Almeida-Thouless instability in short-range Ising spin-glasses
| Autor: | Singh, R. R. P., Young, A. P. |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 96, 012127 (2017) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.96.012127 |
| Popis: | 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 $d=5$. Comment: 5 pages and 5 figures. Series coefficients in Supplementary Materials |
| Databáze: | arXiv |
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