Abstract
We consider infinite or periodic 2D triangular Ising lattices with arbitrary positive or negative nearest-neighbor couplings , where and i indicate the bond position and orientation, respectively. Iterative application of the star–triangle transformation to an initial lattice with a set of couplings generates a sequence of lattices , for n = 1, 2, …, with couplings . When includes sufficiently strongly frustrated plaquettes, complex couplings will appear. We show that, nevertheless, the variables remain confined to the union of the real and the imaginary axis. The same holds for a lattice with free boundaries, provided we distinguish between ‘receding’ and ‘advancing’ boundaries, the latter having degrees of freedom that must be fixed by an appropriately chosen protocol. This study establishes a framework for future analytic and numerical work on such frustrated Ising lattices.
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