Finite-size critical scaling in Ising spin glasses in the mean-field regime

Abstract

We study in Ising spin glasses the finite-size effects near the spin-glass transition in zero field and at the de Almeida-Thouless transition in a field by Monte Carlo methods and by analytical approximations. In zero field, the finite-size scaling function associated with the spin-glass susceptibility of the Sherrington-Kirkpatrick mean-field spin-glass model is of the same form as that of one-dimensional spin-glass models with power-law long-range interactions in the regime where they can be a proxy for the Edwards-Anderson short-range spin-glass model above the upper critical dimension. We also calculate a simple analytical approximation for the spin-glass susceptibility crossover function. The behavior of the spin-glass susceptibility near the de Almeida-Thouless transition line has also been studied, but here we have only been able to obtain analytically its behavior in the asymptotic limit above and below the transition. We have also simulated the one-dimensional system in a field in the non-mean-field regime to illustrate that when the Imry-Ma droplet length scale exceeds the system size one can then be erroneously lead to conclude that there is a de Almeida-Thouless transition even though it is absent.

arXiv comment10 pages, 7 figures

References in corpus (33)

• Critical Behavior of the Three-Dimensional Ising Spin Glass
• Universality in three-dimensional Ising spin glasses: A Monte Carlo study
• Non-Mean-Field Behavior of Realistic Spin Glasses
• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Diluted one-dimensional spin glasses with power law decaying interactions
• Ordering and Broken Symmetry in Short-Ranged Spin Glasses
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Probing the Almeida-Thouless line away from the mean-field model
• Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses
• Disappearance of the de Almeida-Thouless line in six dimensions
• The Complexity of Ising Spin Glasses
• Ising spin glass transition in magnetic field out of mean-field
• Spin glasses in a field: Three and four dimensions as seen from one space dimension
• Replica symmetry breaking in and around six dimensions
• Finite-size scaling above the upper critical dimension
• Theory of minimum spanning trees I: Mean-field theory and strongly disordered spin-glass model
• Finite size scaling of the correlation length above the upper critical dimension
• The correspondence between long-range and short-range spin glasses
• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
• The de Almeida-Thouless line in vector spin glasses
• Geometry of large-scale low-energy excitations in the one-dimensional Ising spin glass with power-law interactions
• Non-perturbative effects in spin glasses
• Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses
• Modified TAP equations for the SK spin glass
• Spin glasses in the non-extensive regime
• Spin glasses and algorithm benchmarks: A one-dimensional view
• The 1/m expansion in spin glasses and the de Almeida-Thouless line
• Spatial correlation functions in 3-d Ising spin glasses
• Bond diluted Levy spin-glass model and a new finite size scaling method to determine a phase transition
• Extreme Value Statistics Distributions in Spin Glasses
• Critical Point Scaling of Ising Spin Glasses in a Magnetic Field
• Hierarchical spin glasses in a magnetic field: A renormalization-group study
• Nature of perturbation theory in spin glasses

Cited by in corpus (13)

• Absence of Marginal Stability in a Structural Glass
• Quantum annealing for the number partitioning problem using a tunable spin glass of ions
• Low-temperature anomalies of a vapor deposited glass
• Unexpected upper critical dimension for spin glass models in a field predicted by the loop expansion around the Bethe solution at zero temperature
• 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
• Study of the de Almeida-Thouless (AT) line in the one-dimensional diluted power-law XY spin glass
• Nature of spin glass order in physical dimensions
• Finite-temperature topological transitions in the presence of quenched uncorrelated disorder
• Probability Theory in Statistical Physics, Percolation, and Other Random Topics: The Work of C. Newman
• Exact finite-size scaling of the maximum likelihood spectra in the quenched and annealed Sherrington-Kirkpatrick spin glass
• Effects of quenched disorder in three-dimensional lattice ${\mathbb{Z}}_2$ gauge Higgs models