Abstract
The authors study the manifold of fixed points of the generalized weak-graph transformation on lattices of even coordination number for the most general vertex model respecting spin-flip symmetry. They conjecture these fixed points to be the loci of phase transitions. As an example, they turn to coordination number six and find phase transitions in certain regions of the manifold of fixed points: first by investigating a gauge-invariant Ising model on a three-dimensional SC lattice with the help of Monte-Carlo simulations; and second for the ice-type zero-field ferroelectric model, in which the transition between frozen ordered and disordered phase is of first order.
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