1997/12/19 by L. G. Tilstra, M. H. Ernst, Tilstra, L. G. +1
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/9712237
39 pages, 11 figures. Submitted to J. Phys. A
arxiv created 1997/12/19 · openalex publication_date 1997/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as density profiles and spatial and temporal correlation functions for models with a dynamics that is updated in (random) sequential and sublattice-parallel order. Here we consider fully parallel or synchronous dynamics, for which only partial results are known, due to the appearance of complicated strong short range correlations, that invalidate simple mean field approximations. This paper is based on two new ingredients: (i) a microscopic characterization of order parameters and local configurations in the relevant phases, based on the microdynamics of the model, and (ii) an improved mean field approximation, which neglects certain four point - and higher order correlation functions. It is conjectured that the density profiles, obtained here, are exact up to terms that are exponentially small in the system size.