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The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media (1009.3725v2)
Published 20 Sep 2010 in cond-mat.dis-nn and cond-mat.other
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.