Ensemble renormalization group for disordered systems

Abstract

We propose and study a renormalization group transformation that can be used also for models with strong quenched disorder, like spin glasses. The method is based on a mapping between disorder distributions, chosen such as to keep some physical properties (e.g., the ratio of correlations averaged over the ensemble) invariant under the transformation. We validate this ensemble renormalization group by applying it to the hierarchical model (both the diluted ferromagnetic version and the spin glass version), finding results in agreement with Monte Carlo simulations.

7 pages, 10 figures

References in corpus (7)

• The critical behavior of three-dimensional Ising spin glass models
• Diluted one-dimensional spin glasses with power law decaying interactions
• Replica symmetry breaking in and around six dimensions
• The correspondence between long-range and short-range spin glasses
• Real space Renormalization Group analysis of a non-mean field spin-glass
• Overlap Interfaces in Hierarchical Spin-Glass models
• Nonlinear Aspects of the Renormalization Group Flows of Dyson's Hierarchical Model

Cited by in corpus (29)

• PCA meets RG
• Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions
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• Unexpected upper critical dimension for spin glass models in a field predicted by the loop expansion around the Bethe solution at zero temperature
• Real Space Renormalization Group Theory of Disordered Models of Glasses
• Real Space Migdal-Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment
• Meta-stable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network
• Hierarchical spin glasses in a magnetic field: A renormalization-group study
• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
• Ensemble renormalization group for the random field hierarchical model
• Free-energy bounds for hierarchical spin models
• One-dimensional Ising spin-glass with power-law interaction : real-space renormalization at zero temperature
• The Ising Spin Glass in dimension four
• Critical Exponents of the Random Field Hierarchical Model
• Evidence for non-universal scaling in dimension four Ising spin glasses
• Dyson hierarchical quantum ferromagnetic Ising chain with pure or random transverse fields
• The bimodal Ising spin glass in dimension two : the anomalous dimension $\eta$
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Critical exponents of the spin glass transition in a field at zero temperature
• Ising Spin Glasses in dimension five
• Multiscaling in the 3D critical site-diluted Ising ferromagnet
• Real-space renormalization-group methods for hierarchical spin glasses
• Statistical mechanics of the spherical hierarchical model with random fields
• Comment on "Real-space renormalization-group methods for hierarchical spin glasses"
• Overlap renormalization group transformations for disordered systems
• Reply to comment on 'Real-space renormalization-group methods for hierarchical spin glasses'
• Order parameter for non-mean-field spin glasses
• Long-range spin glass in a field at zero temperature