2001/02/01 by Alberto Rosso, Werner Krauth · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Dynamic Monte Carlo method #Elasticity (physics) #Ergodic theory #Geometry #Hybrid Monte Carlo #Kinetic Monte Carlo #Markov chain Monte Carlo #Material Dynamics and Properties #Mathematical analysis #Mathematics #Monte Carlo method #Monte Carlo method in statistical physics #Monte Carlo molecular modeling #Physics #Physics of Superconductivity and Magnetism #Scaling #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.65.012202
published as Phys. Rev. B 65, 012202 (2001) · 4 pages, 3 figures
arxiv created 2001/02/01 · arxiv updated 2009/11/30
We show that the common local Monte Carlo rules used to simulate the motion of driven elastic strings in disordered media cannot capture the interplay between elasticity and disorder which lies at the heart of these systems. We therefore discuss a class of generalized Monte Carlo algorithms where an arbitrary number of line elements may move at the same time. We prove that all these dynamical rules have the same value of the critical force and possess phase spaces made up of a single ergodic component. A variant Monte Carlo algorithm allows us to compute the critical force of a sample in a single pass through the system. We establish dynamical scaling properties and obtain precise values for the critical force, which is finite even for an unbounded distribution of the disorder. Extensions to higher dimensions are outlined.