Spin glass transition in a magnetic field: a renormalization group study

Abstract

We study the transition of short range Ising spin glasses in a magnetic field, within a general replica symmetric field theory, which contains three masses and eight cubic couplings, that is defined in terms of the fields representing the replicon, anomalous and longitudinal modes. We discuss the symmetry of the theory in the limit of replica number n to 0, and consider the regular case where the longitudinal and anomalous masses remain degenerate. The spin glass transitions in zero and non-zero field are analyzed in a common framework. The mean field treatment shows the usual results, that is a transition in zero field, where all the modes become critical, and a transition in non-zero field, at the de Almeida-Thouless (AT) line, with only the replicon mode critical. Renormalization group methods are used to study the critical behavior, to order epsilon = 6-d. In the general theory we find a stable fixed-point associated to the spin glass transition in zero field. This fixed-point becomes unstable in the presence of a small magnetic field, and we calculate crossover exponents, which we relate to zero-field critical exponents. In a finite magnetic field, we find no physical stable fixed-point to describe the AT transition, in agreement with previous results of other authors.

36 pages with 4 tables. To be published in Phys. Rev. B

References in corpus (3)

• Generic replica symmetric field-theory for short range Ising spin glasses
• Ising Spin Glasses in a Magnetic Field
• Zero-temperature responses of a 3D spin glass in a field

Cited by in corpus (39)

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• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
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• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Marginal stability of soft anharmonic mean field spin glasses
• On the two-steps relaxation of mean-field glasses: p-spin model
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• Numerical study of the SK Model in magnetic field
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• The kinetic spherical model in a magnetic field
• Almeida-Thouless transition below six dimensions
• Functional renormalization group for multilinear disordered Langevin dynamics I: Formalism and first numerical investigations at equilibrium
• Absence of an equilibrium ferromagnetic spin glass phase in three dimensions
• On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance
• Hierarchical spin glasses in a magnetic field: A renormalization-group study
• Replica symmetric spin glass field theory
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• Numerical test of the replica-symmetric Hamiltonian for the correlations of the critical state of spin glasses in a field
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• Spin-glass dynamics: experiment, theory and simulation
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