Some considerations of finite dimensional spin glasses

Abstract

In talk I will review the theoretical results that have been obtained for spin glasses, paying a particular attention to finite dimensional spin glasses. I will concentrate my attention on the formulation of the mean field approach and on its numerical and experimental verifications. I will mainly considered equilibrium properties at zero magnetic field, where the situation is clear and it should be not controversial. I will present the various hypothesis at the basis of the theory and I will discuss their physical status.

Contribution to the conference "Viewing the World through Spin Glasses" in honour of Professor David Sherrington on the occasion of his 65th birthday, 31 August - 1 September 2007. 16 pages, 8 figures

References in corpus (39)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
• An Extended Variational Principle for the SK Spin-Glass Model
• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• Fluctuation-dissipation ratio of a spin glass in the aging regime
• Nature of the Spin Glass State
• Spin and link overlaps in 3-dimensional spin glasses
• On the Stability of the Quenched State in Mean Field Spin Glass Models
• Numerical Evidence for Spontaneously Broken Replica Symmetry in 3D Spin Glasses
• The response of glassy systems to random perturbations: A bridge between equilibrium and off-equilibrium
• Absence of an Almeida-Thouless line in Three-Dimensional Spin Glasses
• Probing the Almeida-Thouless line away from the mean-field model
• About the overlap distribution in mean field spin glass models
• Interfaces and Lower Critical Dimension in a Spin Glass Model
• Off-Equilibrium Dynamics at Very Low Temperatures in 3d Spin Glasses
• On the Effects of a Bulk Perturbation on the Ground State of 3D Ising Spin Glasses
• On the Effects of Changing the Boundary Conditions on the Ground State of Ising Spin Glasses
• Magnetic Relaxation Phenomena in a CuMn Spin Glass
• Ultrametricity in the Edwards-Anderson Model
• Zero-temperature responses of a 3D spin glass in a field
• On the origin of ultrametricity
• Numerical Simulations of the 4D Edwards-Anderson Spin Glass with Binary Couplings
• Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses
• On the Dynamics of the 4d Spin Glass in a magnetic field
• Lack of Ultrametricity in the Low-Temperature phase of 3D Ising Spin Glasses
• Simulation of 3d Ising spin glass model using three replicas: study of Binder cumulants
• Critical Behavior of the 4D Spin Glass in Magnetic Field
• Overlap Equivalence in the Edwards-Anderson Model
• Replica equivalence in the Edwards-Anderson model
• 4D Spin Glasses in Magnetic Field Have a Mean Field like Phase
• Replica field theory and renormalization group for the Ising spin glass in an external magnetic field
• Ultrametricity in 3D Edwards-Anderson spin glasses
• A Numerical Study of Ultrametricity in Finite Dimensional Spin Glasses
• Comment on "Ising Spin Glasses in a Magnetic Field"
• Spatial correlation functions in 3-d Ising spin glasses
• Scaling and infrared divergences in the replica field theory of the Ising spin glass
• Local overlaps, heterogeneities and the local fluctuation dissipation relations
• Low T Dynamical Properties of Spin Glasses Smoothly Extrapolate to T=0

Cited by in corpus (17)

• Strengths and Weaknesses of Parallel Tempering
• Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions
• Number of thermodynamic states in the three-dimensional Edwards-Anderson spin glass
• Fractal dimension of interfaces in Edwards-Anderson spin glasses for up to six space dimensions
• 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
• Interface free-energy exponent in the one-dimensional Ising spin glass with long-range interactions in both the droplet and broken replica symmetry regions
• Evidence against an Almeida-Thouless line in disordered systems of Ising dipoles
• Multicritical point on the de Almeida-Thouless line in spin glasses in $d>6$ dimensions
• Evidence of many thermodynamic states of the three-dimensional Ising spin glass
• Spatial correlation functions and dynamical exponents in very large samples of 4D spin glasses
• Random-field-induced disordering mechanism in a disordered ferromagnet: Between the Imry-Ma and the standard disordering mechanism
• Free energy barriers in the Sherrington-Kirkpatrick model
• Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass
• Nature of spin glass order in physical dimensions
• On one-step replica symmetry breaking in the Edwards-Anderson spin glass model
• Complex Cooperative Behaviour in Range-free Frustrated Many-body Systems