Disappearance of the de Almeida-Thouless line in six dimensions

Abstract

We show that the Almeida-Thouless line in Ising spin glasses vanishes when their dimension d -> 6 as h_{AT}^2/T_c^2 = C(d-6)^4(1- T/T_c)^{d/2 - 1}, where C is a constant of order unity. An equivalent result which could be checked by simulations is given for the one-dimensional Ising spin glass with long-range interactions. It is shown that replica symmetry breaking also stops as d -> 6.

Additional text and one figure added

References in corpus (3)

• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Behavior of Ising Spin Glasses in a Magnetic Field
• The ordered phase of the one-dimensional Ising spin glass with long-range interactions

Cited by in corpus (55)

• Absence of Marginal Stability in a Structural Glass
• Perspective: Gardner Physics in Amorphous Solids and Beyond
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Janus II: a new generation application-driven computer for spin-system simulations
• Replica symmetry breaking in and around six dimensions
• Nature of excitations and defects in structural glasses
• The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority
• Nontrivial critical fixed point for replica-symmetry-breaking transitions
• The Gardner transition in physical dimensions
• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
• Dynamical transition in the D = 3 Edwards-Anderson spin glass in an external magnetic field
• The Gardner transition in finite dimensions
• Hierarchical landscape of hard disk glasses
• Renormalization group analysis of the M-p-spin glass model with p=3 and M=3
• Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class
• Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking
• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• Origin of the Growing Length Scale in M-p-Spin Glass Models
• One-step replica-symmetry-breaking phase below the de Almeida-Thouless line in low-dimensional spin glasses
• Unexpected upper critical dimension for spin glass models in a field predicted by the loop expansion around the Bethe solution at zero temperature
• Non-perturbative effects in spin glasses
• Replica Fourier Transform: Properties and Applications
• One-dimensional infinite component vector spin glass with long-range interactions
• Fractal dimension of interfaces in Edwards-Anderson spin glasses for up to six space dimensions
• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• Renormalization Group on hierarchical lattices in finite dimensional disordered Ising and Blume-Emery-Griffiths Models
• The Fractal Dimension of Interfaces in Edwards-Anderson and Long-range Ising Spin Glasses: Determining the Applicability of Different Theoretical Descriptions
• The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited
• Real Space Migdal-Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment
• An exploratory study of the glassy landscape near jamming
• The 1/m expansion in spin glasses and the de Almeida-Thouless line
• Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions
• Hierarchical spin glasses in a magnetic field: A renormalization-group study
• 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
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
• Learning to find order in disorder
• Multicritical point on the de Almeida-Thouless line in spin glasses in $d>6$ dimensions
• Inherent Structures in m-component Spin Glasses
• Spin-glass dynamics: experiment, theory and simulation
• Physical observables of the Ising spin glass in 6-epsilon dimensions: asymptotical behavior around the critical fixed point
• Possible instability of one-step replica symmetry breaking in p-spin Ising models outside mean-field theory
• Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field
• One-loop topological expansion for spin glasses in the large connectivity limit
• Self-organized critical behavior and marginality in Ising spin glasses
• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
• Bethe $M$-layer construction on the Ising model
• Critical exponents of the spin glass transition in a field at zero temperature
• Comment on "Critical point scaling of Ising spin glasses in a magnetic field" by J. Yeo and M.A. Moore
• Replica Symmetry and Replica Symmetry Breaking for the Traveling Salesperson Problem
• Why replica symmetry breaking does not occur below six dimensions in Ising spin glasses
• The Gardner correlation length scale in glasses
• Reply to "Comment on "Critical Point Scaling of Ising Spin Glasses in a Magnetic Field" "
• Evidence of de Almeida-Thouless line below six dimensions
• Long-range spin glass in a field at zero temperature