Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-09-20
Physics
Condensed Matter
Disordered Systems and Neural Networks
Scientific paper
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.
Dimitrova Ol'ga
Mezard Marc
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