\sqrt3×\sqrt3 Structure on the Triangular Lattice

Abstract

An Ising model with nearest neighbor antiferromagnetic and next nearest neighbor ferromagnetic interactions is studied by the phenomenological renormalization method. The phase transition to the \sqrt3×\sqrt3 structure is of the second order for weak fields, and the critical exponents y_T≅1.2 and η≅0.30 are consistent with the conjectured values of the 3-state Potts model. Beyond a tricritical point the transition becomes of the first order for strong fields. The tricritical exponent y_{T, t}≅1.73 and η_t≅0.21 are also in agreement with the 3-state Potts tricritical values y_T,t^3P=12⁄7 and η_t^3P=4⁄21. The XY-like phase transition at zero fields, which was obtained by the Monte Carlo simulations, is not found in the present calculation.