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We propose a mechanism for the crossover between first-order and continuous transitions in confined liquid crystals that is based on a dimensional crossover of both the space and the order-parameter variables. We estimate the relevant parameters by carrying out explicit mean-field calculations of the global phase diagram of an appropriate lattice model. We discuss in some detail the effects on the phase diagram of the fluctuations neglected by the mean-field approximation.
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Gama et al. (1990) studied this question.
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