Ensemble renormalization group for the random field hierarchical model

Abstract

The Renormalization Group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple models. In this work we study a real-space RG transformation on the Dyson hierarchical lattice with a random field, which led to a reconstruction of the RG flow and to an evaluation of the critical exponents of the model at T = 0. We show that this method gives very accurate estimations of the critical exponents, by comparing our results with the ones obtained by some of us using an independent method.

References in corpus (3)

• Multicritical points for the spin glass models on hierarchical lattices
• Overlap Interfaces in Hierarchical Spin-Glass models
• Random field Ising model : statistical properties of low-energy excitations and of equilibrium avalanches

Cited by in corpus (9)

• Many-Body Localization : construction of the emergent local conserved operators via block real-space renormalization
• Real Space Renormalization Group Theory of Disordered Models of Glasses
• Meta-stable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network
• Dyson Hierarchical Long-Ranged Quantum Spin-Glass via real-space renormalization
• Critical Exponents of the Random Field Hierarchical Model
• Existence of long-range order in random-field Ising model on Dyson hierarchical lattice
• Real-space renormalization-group methods for hierarchical spin glasses
• The Hierarchical Parity Model
• Statistical mechanics of the spherical hierarchical model with random fields