Real-Space Renormalization group for spin glasses

TL;DR

This paper reviews real-space Renormalization Group methods applied to finite-dimensional spin glasses, discussing their strengths and weaknesses in understanding phase transitions and critical behavior.

Contribution

It provides a comprehensive review of RG techniques for spin glasses, emphasizing their capabilities and limitations in finite dimensions.

Findings

RG methods reveal complex transition behaviors in spin glasses.

Strengths and weaknesses of RG approaches are critically analyzed.

Insights into finite-dimensional spin glass phase transitions are discussed.

Abstract

While in the fully-connected limit the solution of the spin-glass model is known, with the existence of a complex transition on a critical line in the temperature-external field phase diagram, in finite dimensions we don't know if a transition is present or not and, if present, if its nature is the same as the one in infinite dimensions. This work contains a review of the real-space Renormalization Group methods that have been applied to Spin Glasses, highlighting both their point of strength and weakness in characterizing the finite dimensional behaviour of the model.