2002/10/17 by E. J. Beamond, Beamond, E. J., A. L. Owczarek +3 · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.mes-hall #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0210359
11 pages, 8 figures
arxiv created 2003/08/19 · arxiv updated 2009/11/30
We consider a network model, embedded on the Manhattan lattice, of a quantum localisation problem belonging to symmetry class C. This arises in the context of quasiparticle dynamics in disordered spin-singlet superconductors which are invariant under spin rotations but not under time reversal. A mapping exists between problems belonging to this symmetry class and certain classical random walks which are self-avoiding and have attractive interactions; we exploit this equivalence, using a study of the classical random walks to gain information about the corresponding quantum problem. In a field-theoretic approach, we show that the interactions may flow to one of two possible strong coupling regimes separated by a transition: however, using Monte Carlo simulations we show that the walks are in fact always compact two-dimensional objects with a well-defined one-dimensional surface, indicating that the corresponding quantum system is localised.