Surface phase transitions: Roughening, preroughening, orientational roughening, and reconstruction in an isotropic frustrated Ising model.

Abstract

We study the roughening, the preroughening, and the orientational roughening transitions for interfaces between phases in the isotropic competing Ising Hamiltonian H=-J${\mathrm{\ensuremath{\Sigma}}}_{\mathit{nm}}$${\mathit{s}}_{\mathit{i}}$${\mathit{s}}_{\mathit{j}}$-2M ${\mathrm{\ensuremath{\Sigma}}}_{\mathit{lnnn}}$${\mathit{s}}_{\mathit{i}}$${\mathit{s}}_{\mathit{j}}$. The symbols, NN, DNN, and LNNN represent nearest-neighbor, diagonal-nearest-neighbor, and linear-next-nearest-neighbor pairs, respectively, with Jg0 and -\ensuremath{\infty}M\ensuremath{\infty}. By performing low-temperature expansions in the three-dimensional cubic lattice, it is found that the roughening transition curve passes through the region in which paramagnetic, ferromagnetic, and modulated phases merge, and is parallel to the phase boundary of ferromagnetic and modulated phases. It is also found that crossover behavior occurs in the roughening transition from the surface tension dominant regime to the bending-energy dominant regime. We examine the preroughening transition for the case of the restricted solid-on-solid (RSOS) model. The preroughening transition line is found to be distinct from the roughening transition line. This confirms the recent prediction by den Nijs [Phys. Rev. Lett. 64, 435 (1990)]. Within the RSOS model, we find a multistate point for reconstructed surface structures. This is analogous to the multistate point in the bulk phase diagram. The orientational roughening transition is also examined. However, it was not possible to obtain the orientational roughening transition line at a temperature higher than that of the translational roughening transition, presumably due to the limited order of the low-temperature series. The results deduced from the low-temperature expansions are compared to the sine-Gordon renormalization-group calculations based on the SOS and RSOS models. Finally we discuss the implications of the surface structure, and the connections with bulk structure.