Abstract
We use high-temperature series expansions to study the Ising spin glass in a magnetic field in -dimensional hypercubic lattices for and in the infinite-range Sherrington-Kirkpatrick (SK) model. The expansions are obtained in the variable for arbitrary values of complete to order . We find that the scaling dimension associated with the ordering-field equals 2 in the SK model and for . However, in agreement with the work of Fisher and Sompolinsky [Phys. Rev. Lett. 54, 1063 (1985)], there is a violation of scaling in a finite field, leading to an anomalous dependence of the de Almeida–Thouless (AT) [J. Phys. A 11, 983 (1978)] line in high dimensions, whereas scaling is restored as . Within the convergence of our series analysis, we present evidence supporting an AT line in . In , the exponents and are substantially larger than mean-field values, but we do not see clear evidence for the AT line in .
- Received 2 May 2017
DOI:https://doi.org/10.1103/PhysRevE.96.012127
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