The 1/m expansion in spin glasses and the de Almeida-Thouless line

Abstract

It is shown by means of a 1/m expansion about the large-m limit of the m-vector spin glass that the lower critical dimension of the de Almeida-Thouless line in spin glasses is equal to the lower critical dimension of the large-m limit of the m-vector spin glass. Numerical studies suggest that this is close to six.

8 pages

References in corpus (7)

• Disappearance of the de Almeida-Thouless line in six dimensions
• Behavior of Ising Spin Glasses in a Magnetic Field
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Replica symmetry breaking in and around six dimensions
• The de Almeida-Thouless line in vector spin glasses
• One-dimensional infinite component vector spin glass with long-range interactions
• Generalised Bose-Einstein phase transition in large-$m$ component spin glasses

Cited by in corpus (13)

• Origin of the Growing Length Scale in M-p-Spin Glass Models
• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• Disorder-free spin glass transitions and jamming in exactly solvable mean-field models
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions
• Critical Point Scaling of Ising Spin Glasses in a Magnetic Field
• Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass
• Learning to find order in disorder
• Inherent Structures in m-component Spin Glasses
• Field theory for zero temperature soft anharmonic spin glasses in a field
• Physical observables of the Ising spin glass in 6-epsilon dimensions: asymptotical behavior around the critical fixed point
• Evidence that the AT transition disappears below six dimensions
• Replica Symmetry Broken States of some Glass Models