Structure factors associated with melting of a p(22) ordered phase on a honeycomb lattice gas: Possible critical scattering at a first-order transition

We study the order-disorder transition of a p(2×2) ordered state on a honeycomb lattice using Monte Carlo calculations of the structure factor. We observe a correlation length which gets large as the transition is approached; the effective critical exponents are close to the exponents characterizing a discontinuity fixed point and similar to those we observe for the first-order transition of the eight-state Potts model. We also discuss how observation of the outer integral-order diffraction beams gives information about the relevance of the field which distinguishes the two triangular sublattices of the honeycomb lattice.