Search for a Kosterlitz-Thouless transition in a triangular Ising antiferromagnet with further-neighbor ferromagnetic interactions

We investigate an antiferromagnetic triangular Ising model with anisotropic ferromagnetic interactions between further neighbors, originally proposed by Kitatani and Oguchi [J. Phys. Soc. Jpn. 57, 1344 (1988)]. The phase diagram as a function of temperature and the ratio between first- and second-neighbor interaction strengths is thoroughly examined. We search for a Kosterlitz-Thouless transition to a state with algebraic decay of correlations, calculating the correlation lengths on strips of width up to 15 sites by transfer-matrix methods. Phenomenological renormalization, conformal invariance arguments, the Roomany-Wyld approximation, and a direct analysis of the scaled mass gaps are used. Our results provide limited evidence that a Kosterlitz-Thouless phase is present. Alternative scenarios are discussed.