Multicritical Point on the de Almeida-Thouless Line in Spin Glasses in d>6 Dimensions

M. A. Moore, N. Read

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    Abstract

    The de Almeida-Thouless (AT) line in Ising spin glasses is the phase boundary in the temperature T and magnetic field h plane below which replica symmetry is broken. Using perturbative renormalization group (RG) methods, we show that, when the dimension d of space is just above six, there is a multicritical point (MCP) on the AT line, which separates a low-field regime, in which the critical exponents have mean-field values, from a high-field regime, where the RG flows run away to infinite coupling strength; as d approaches six from above, the MCP approaches the zero-field critical point exponentially in 1/(d-6). Thus, on the AT line, perturbation theory for the critical properties breaks down at a sufficiently large magnetic field even above 6 dimensions, as well as for all nonzero fields when d≤6, as was known previously. We calculate the exponents at the MCP to first order in μ=d-6>0. The fate of the MCP as d increases from just above six to infinity is not known.

    Original languageEnglish
    Article number130602
    JournalPhysical Review Letters
    Volume120
    Issue number13
    Early online date28 Mar 2018
    DOIs
    Publication statusPublished - 2018

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