Unbinding transition in semi-infinite two-dimensional localized systems

Article

关键词: POLYNUCLEAR GROWTH-MODEL;    DISORDERED-SYSTEMS;    PROBABILITY-DISTRIBUTIONS;    UNIVERSAL DISTRIBUTIONS;    LIMITING DISTRIBUTIONS;    DIRECTED POLYMER;    RANDOM MATRICES;    1+1 DIMENSIONS;    KPZ EQUATION;    FREE-ENERGY;   

DOI  :  10.1103/PhysRevB.91.155413

来源: SCIE

【 摘 要 】

We consider a two-dimensional strongly localized system defined in a half-plane and whose transfer integral in the edge can be different than in the bulk. We predict an unbinding transition, as the edge transfer integral is varied, from a phase where conduction paths are distributed across the bulk to a bound phase where propagation is mainly along the edge. At criticality the logarithm of the conductance follows the F-1 Tracy-Widom distribution. We verify numerically these predictions for both the Anderson and the Nguyen, Spivak, and Shklovskii models. We also check that for a half-plane, i.e., when the edge transfer integral is equal to the bulk transfer integral, the distribution of the conductance is the F-4 Tracy-Widom distribution. These findings are strong indications that random sign directed polymer models and their quantum extensions belong to the Kardar-Parisi-Zhang universality class. We have analyzed finite-size corrections at criticality and for a half-plane.

【 授权许可】

Free