Determination of the Critical Points of Antiferromagnetic Ising Model with Next Nearest Neighbour Interactions on the Triangular Lattice

Abstract

Positions of critical temperatures of antiferromagnetic Ising model with ferromagnetic next nearest neighbour interactions on the triangular lattice are investigated by making use of their properties of the Kosterlitz-Thouless type of phase transition. In particular, finite-size scaling method and Monte Carlo Renormalization Group methods (MCRG) with flow diagrams of the anomalous dimension η show the fixed line structure where the correlation length diverges. Another MCRG with flow diagram of the stiffness constant also shows a critical property clearly. The temperature dependence of the long range order is also discussed in order to locate the lower critical point.