Structure factors associated with the continuous melting of two-dimensional lattice gases: Models with ( sqrt 3 x sqrt 3)R30 degrees and p(2 x 2) ordered states on triangular nets.

Abstract

We study the temperature dependence of the structure factors of two lattice gases which undergo order-disorder phase transitions. Our goal is to determine how much information about the critical behavior of these phase transitions a low-energy electron-diffraction experiment might obtain. We use Monte Carlo simulation to compute the structure factors. Both lattice gases are on triangular nets; one has a (\ensuremath{\surd}3\ifmmode\times\else\texttimes\fi{}\ensuremath{\surd}3)R30\ifmmode^\circ\else\textdegree\fi{} ordered phase; the other has a p(2\ifmmode\times\else\texttimes\fi{}2) ordered phase. The structure factors scale almost halfway from the center of an extra spot to the zone center; for system sizes comparable to those that are physically realizable we see effective critical exponents which are typically within of order 10% of expectations based on universality. Below the transition temperature, nonlinearities in log-log plots are significant, indicating that corrections to scaling cannot be ignored. We consider how asymmetries in the structure factor reflect differences between lattice-gas systems and magnetic analogs in the same universality class and also briefly treat the effects of quenched random vacancies and of a fixed concentration of annealed vacancies.