The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media
Disordered Systems and Neural Networks
2015-05-20 v2 Other Condensed Matter
Abstract
After reviewing the basics of the cavity method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of spins with random ferromagnetic interactions and a random transverse field. The quantum cavity equations describing the ferromagnetic-paramagnetic phase transition can be transformed into the well-known problem of a classical directed polymer in a random medium. The glass transition of this polymer problem translates ino the existence of a `Griffith phase' close to the quantum phase transition of the quantum spin problem, where the physics is dominated by rare events.
Cite
@article{arxiv.1009.3725,
title = {The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media},
author = {Olga Dimitrova and Marc Mezard},
journal= {arXiv preprint arXiv:1009.3725},
year = {2015}
}