Exact density profiles for fully asymmetric exclusion process with discrete-time dynamics

Exact density profiles in the steady state of the one-dimensional fully asymmetric simple exclusion process on semi-infinite chains are obtained in the case of forward-ordered sequential dynamics by taking the thermodynamic limit in our recent exact results for a finite chain with open boundaries. The corresponding results for sublattice parallel dynamics follow from the relationship obtained by Rajewsky and Schreckenberg [Physica A 245, 139 (1997)] and for parallel dynamics from the mapping found by Evans, Rajewsky and Speer [J. Stat. Phys. 95, 45 (1999)]. By comparing the asymptotic results appropriate for parallel update with those published in the latter paper, we correct some technical errors in the final results given there.Comment: About 10 pages and 3 figures, new references are added and a comparison is made with the results by de Gier and Nienhuis [Phys. Rev. E 59, 4899(1999)

On the finite-size behavior of systems with asymptotically large critical shift

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.Comment: 24 pages, late