Random Walks and Anderson Localisation in a Three-Dimensional Class C Network Model
(2009)
Random Walks and Anderson Localisation in a Three-Dimensional Class C Network Model
ArXiv 0810.5105 (2008)
Abstract:
We study the disorder-induced localisation transition in a three-dimensional network model that belongs to symmetry class C. The model represents quasiparticle dynamics in a gapless spin-singlet superconductor without time-reversal invariance. It is a special feature of network models with this symmetry that the conductance and density of states can be expressed as averages in a classical system of dense, interacting random walks. Using this mapping, we present a more precise numerical study of critical behaviour at an Anderson transition than has been possible previously in any context.SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model.
Phys Rev Lett 101:15 (2008) 155702
Abstract:
We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model
(2008)
Structural phase transitions in geometrically frustrated antiferromagnets
(2008)