Non-perturbative effects in spin glasses

Abstract

We present a numerical study of an Ising spin glass with hierarchical interactions - the hierarchical Edwards-Anderson model with an external magnetic field (HEA). We study the model with Monte Carlo (MC) simulations in the mean-field (MF) and non-mean-field (NMF) regions corresponding to $d\ge 4$ and $d<4$ for the $d$-dimensional ferromagnetic Ising model respectively. We compare the MC results with those of a renormalization-group (RG) study where the critical fixed point is treated as a perturbation of the MF one, along the same lines as in the $\epsilon$-expansion for the Ising model. The MC and the RG method agree in the MF region, predicting the existence of a transition and compatible values of the critical exponents. Conversely, the two approaches markedly disagree in the NMF case, where the MC data indicates a transition, while the RG analysis predicts that no perturbative critical fixed point exists. Also, the MC estimate of the critical exponent $\nu$ in the NMF region is about twice as large as its classical value, even if the analog of the system dimension is within only $\sim 2\%$ from its upper-critical-dimension value. Taken together, these results indicate that the transition in the NMF region is governed by strong non-perturbative effects.

References in corpus (19)

• Critical Behavior of the Three-Dimensional Ising Spin Glass
• Universal Finite Size Scaling Functions in the 3D Ising Spin Glass
• Spin and link overlaps in 3-dimensional spin glasses
• P-adic numbers and replica symmetry breaking
• Study of the de Almeida-Thouless line using power-law diluted one-dimensional Ising spin glasses
• Probing the Almeida-Thouless line away from the mean-field model
• Disappearance of the de Almeida-Thouless line in six dimensions
• Ising spin glass transition in magnetic field out of mean-field
• Thermodynamic glass transition in a spin glass without time-reversal symmetry
• Replica symmetry breaking in and around six dimensions
• Spin glass transition in a magnetic field: a renormalization group study
• Energetics and geometry of excitations in random systems
• Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass
• Ising Spin Glasses in a Magnetic Field
• Critical behaviour and ultrametricity of Ising spin-glass with long-range interactions
• Overlap Interfaces in Hierarchical Spin-Glass models
• Replica field theory and renormalization group for the Ising spin glass in an external magnetic field
• A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model
• Hierarchical spin glasses in a magnetic field: A renormalization-group study

Cited by in corpus (7)

• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• Functional renormalization group for multilinear disordered Langevin dynamics I: Formalism and first numerical investigations at equilibrium
• A Multi-Scale Spin-Glass Mean-Field Model
• Hierarchical spin glasses in a magnetic field: A renormalization-group study
• Physical observables of the Ising spin glass in 6-epsilon dimensions: asymptotical behavior around the critical fixed point
• Quantum criticality in photorefractive optics: vortices in laser beams and antiferromagnets
• Order parameter for non-mean-field spin glasses