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arXiv · 1211.7297

Spin glasses in a field: Three and four dimensions as seen from one space dimension

Derek Larson·Helmut G. Katzgraber·M. A. Moore·A. P. Young
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Abstract

We study the existence of a line of transitions of an Ising spin glass in a magnetic field-known as the de Almeida-Thouless line-using one-dimensional power-law diluted Ising spin-glass models. We choose the power-law exponent to have values that approximately correspond to three- and four-dimensional nearest-neighbor systems and perform a detailed finite-size scaling analysis of the data for large linear system sizes, both using a new approach proposed recently [Phys. Rev. Lett. 103, 267201 (2009)], as well as traditional approaches. Our results for the model corresponding to a three-dimensional system are consistent with there being no de Almeida-Thouless line, although the new finite-size scaling approach does not rule one out. For the model corresponding to four space dimensions, the new and traditional finite-size scaling analyses give conflicting results, indicating the need for a better understanding of finite-size scaling of spin glasses in a magnetic field.

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Derek Larson, Helmut G. Katzgraber, M. A. Moore, A. P. Young. 2013-01-19. Spin glasses in a field: Three and four dimensions as seen from one space dimension. https://doi.org/10.1103/physrevb.87.024414

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