Anisotropic random sequential adsorption of dimers on a square lattice

Abstract

The properties of the anisotropic random sequential adsorption of dimers on a square lattice are determined by Monte Carlo simulation and time-series expansion. The fractions of vertical and horizontal bonds occupied by dimers are calculated as a function of v, the probability of choosing vertical bonds to place dimers. In the limit v→0, the asymptotic fraction of vertical bonds occupied by dimers does not vanish but has the exact value ${\mathit{e}}^{\mathrm{-}2}$[1-exp(-2${\mathit{e}}^{\mathrm{-}2}$)]/2=0.016 046. . . .