Ma-Dasgupta renormalization studies of various disordered systems

TL;DR

This paper reviews Ma-Dasgupta real-space renormalization techniques applied to various disordered systems, providing exact results for classical and quantum models, especially in one dimension, focusing on dynamics, statics, and phase transitions.

Contribution

It offers a comprehensive analysis of Ma-Dasgupta renormalization applied to multiple disordered models, highlighting exact results and phase transition behaviors in one-dimensional systems.

Findings

Exact results for disordered classical and quantum models

Insights into off-equilibrium dynamics and coarsening

Analysis of quantum phase transitions in disordered chains

Abstract

The Ma-Dasgupta real-space renormalization methods allow to study disordered systems which are governed by strong disorder fixed points. After a general introduction to the qualitative ideas and to the quantitative renormalization rules, we describe the explicit exact results that can be obtained in various one-dimensional models, either classical or quantum, either for dynamics or statics. The main part of this dissertation is devoted to statistical physics models, with special attention to (i) the off-equilibrium dynamics of a particle diffusing in a Brownian potential or in a trap landscape, (ii) the coarsening dynamics and the equilibrium of classical disordered spin chains, (iii) the delocalization transition of a random polymer at an interface. The last part of the dissertation deals with two disordered quantum spin chains which exhibit a zero-temperature phase transition as the disorder varies, namely (a) the random antiferromagnetic S=1 spin chain, (b) the random transverse field Ising chain.