Absence of enhanced fluctuations as a first-order phase transition is approached: An exact transfer-matrix study

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Abstract
As a second-order phase transition is traversed critical scattering appears; these fluctuations serve notice of the impending loss of stability of the equilibrium phase. For a model first-order phase transition we rigorously prove, using exact thermodynamic quantities obtained from strip-transfer-matrix calculations, as well as finite-size-scaling analysis, that as a temperature-driven, symmetry-breaking, first-order phase transition is approached, no enhancement of fluctuations into the future product phase occurs. To be specific, we study the probability of occupation of the product phase (stable below the transition temperature), and demonstrate that this is a monotonically decreasing function as the transition temperature is approached from above. The relation of this pedagogical result to x-ray scattering experiments is discussed.