Multicritical point on the de Almeida-Thouless line in spin glasses in $d>6$ dimensions

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 $6$ 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 $6$ from above, the location of 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 sufficiently large magnetic field even above $6$ dimensions, as well as for all non-zero fields when $d\le 6$ as was known previously. We calculate the exponents at the MCP to first order in $\epsilon =d-6>0$. The fate of the MCP as $d$ increases from just above 6 to infinity is not known.

5 pages. V2: published version, minor changes

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Cited by in corpus (6)

• Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class
• One-step replica-symmetry-breaking phase below the de Almeida-Thouless line in low-dimensional spin glasses
• Chaotic temperature and bond dependence of four-dimensional Gaussian spin glasses with partial thermal boundary conditions
• Numerical test of the replica-symmetric Hamiltonian for the correlations of the critical state of spin glasses in a field
• Why replica symmetry breaking does not occur below six dimensions in Ising spin glasses
• Physics of the Edwards-Anderson Spin Glass in Dimensions $d=3,\dots ,8$ from Heuristic Ground State Optimization