Variational theory of preroughening

Saito’s variational mean-field theory of roughening [Y. Saito, Z. Phys B 32, 75 (1978)] is generalized to include preroughening. The starting point is a sine-Gordon Hamiltonian with a cosine parameter changing sign at a temperature $T_{\mathrm{PR}}.$ This theory accounts for a number of known features of preroughening from solid-on-solid lattice models, including logarithmic divergence of the average interface width as a function of the system size and continuous crystal growth at $T_{\mathrm{PR}}.$ When $T_{\mathrm{PR}}$ reduces to one quarter of the roughening temperature or less, preroughening becomes first order. We also consider adsorption over an attractive substrate. Using our variational theory, we calculate adsorption isotherms. They show a reentrant layering pattern, which connects well with observations for noble gases adsorbed on graphite.