Structure factors associated with the melting of a (31) ordered phase on a centered-rectangular lattice gas: Effective scaling in a three-state chiral-clock-like model

By computing the structure factor through the melting transition of a commensurate (3×1) phase in a version of Baxter’s generalized hard hexagon model, we simulate what might be observed in diffraction experiments (especially those using low-energy electrons) on chemisorption systems which have similar Landau-Ginzburg-Wilson Hamiltonians. In the commensurate and disordered phases we observe that the shift of the peak of the critical scattering from the commensurate position is roughly proportional to the inverse correlation length in the reduced temperature range 0.015–0.15. The proportionality constant appears to depend on the position of the transition on the phase boundary (i.e., on the chemical potential). We see no sign of an incommensurate floating phase between the disordered and commensurate phases. Effective critical exponents are consistent with those expected from the three-state Potts model. To the precision of this calculation (a few percent), the structure factor scales over approximately 10% of the Brillouin-zone area.