Pseudo - first - order phase transitions in one dimension

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Abstract
The effect of fluctuations on a Landau-Ginzburg model of a first-order phase transition in one dimension is studied. Extremely sharp pseudotransitions can be obtained. The critical region or width of the transition is found to vanish exponentially with the effective number of interacting units across a cross section of the system. The results are physically interpreted in the context of the Landau-Lifschitz proof that phase equilibrium is impossible in one dimension.