Ordering and Phase Transitions Due to Entropy Gains in Two-Dimensional Frustration Models

Abstract

Layered and isotropic frustration models on a square lattice are studied in a systematic way from the viewpoint of seeing how frustrations affect ordering. Ordering is attributed to entropy gains, which is analysed introducing cluster (C) regions and entropy-yielding (S) regions. These local structures are closely related to excited states with the lowest energy, which is investigated through the configurations of unsatisfied bonds (or strings). Searching for the conditions for local coupling between C regions via a S region and then for global ordering we reach the same results on the ordering for the layered models as those obtained by Hoever et al. For some isotropic models as well as layered ones the temperature dependence of interface tension is calculated. The former models show re-entrant phenomena characteristic of this type of phase transitions. The symmetry of frustration configuration and its breaking are also discussed.