Order-disorder transition in the surface charge-density-wave phase of Cu(001)-c(4x4)-In

We have investigated the x-ray critical scattering from In/Cu(001) near the charge-density-wave phase transition. The critical exponents of the temperature dependence of the order parameter, the susceptibility, and the correlation length of the order parameter fluctuations are in agreement with those expected for a two-dimensional Ising-type phase transition. The lattice transition temperature, Tcl=345 K, is 60 K lower than that for the electronic transition reported recently. The surface phase transition in this system is not well described by conventional weak- or strong-coupling theories, which assume a single characteristic energy gap. It is suggested that the electronic and lattice degrees of freedom on the surface are governed separately by two different energy gaps