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The finite-size broadening of a first-order phase transition is estimated to be proportional to the inverse of the product of the system size and the latent entropy of the transition. The relation to the usual second-order-transition case is discussed. The limit of a small first-order transition is shown to be consistent with a second-order one. These results are relevant both for real and computer experiments on systems that are quite small but larger than microscopic sizes.
Y. Imry (Sat,) studied this question.