Critical behaviour of a lattice model of the nematic to smectic-A transition

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Abstract
The critical behaviour of a lattice version of the de Gennes model of the nematic to smectic-A transition is studied by Monte Carlo simulations. Several features observed in experiments are qualitatively reproduced in the simulations. The model exhibits a continuous phase transition with the specific heat exponent α close to zero. The order-parameter correlation functions show anisotropic critical behaviour as the transition is approached form the nematic side. On the other hand, the observed behaviour of the correlation functions in the superconducting gauge strongly indicates an isotropic critical point for both small and large values of the splay elastic constant. The observed behaviour of the twist and bend elastic constants is consistent with this conclusion. The gauge-dependence of the correlation functions appears to be well-described by the decoupling approximation proposed by Lubensky and co-workers