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