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We investigate an antiferromagnetic triangular Ising model with anisotropicferromagnetic interactions between next-nearest neighbours, originally proposedby Kitatani and Oguchi (J. Phys. Soc. Japan {\bf 57}, 1344 (1988)). The phasediagram as a function of temperature and the ratio between first- and second-neighbour interaction strengths is thoroughly examined. We search for aKosterlitz-Thouless transition to a state with algebraic decay of correlations,calculating the correlation lengths on strips of width up to 15 sites bytransfer-matrix methods. Phenomenological renormalization, conformal invariancearguments, the Roomany-Wyld approximation and a direct analysis of the scaledmass gaps are used. Our results provide limited evidence that aKosterlitz-Thouless phase is present. Alternative scenarios are discussed.Comment: 10 pages, RevTeX 3; 11 Postscript figures (uuencoded); to appear in  Phys. Rev. E (1995

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