Critical behaviour of a two-dimensional bonded lattice model

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Abstract
The Bell-Lavis model (1970) of a two-dimensional bonded lattice fluid is investigated by real space renormalisation group methods. All the fixed points in a restricted parameter subspace are obtained, but their stability is analysed in the full parameter space of the system. Within the subspace melting is predicted to occur via a second-order transition in the same universality class as the 3-state ferromagnetic Potts model. This contrasts with the predictions of mean-field theory. There is however a weakly relevant eigenvalue whose corresponding eigenvector is in a direction out of the subspace, so the fixed point may not be a critical point for the full model. A second result of interest is that the fixed point, found by Schick and Griffiths (1977) for the 3-state antiferromagnetic Potts model on a triangular lattice, also describes the transition in the more general case of an antiferromagnetic spin-one Ising model (the Blume-Emery-Griffiths model) on the same lattice. Some interesting symmetry properties of the subspace are also discussed.