ABSENCE OF ENHANCED FLUCTUATIONS AS A 1ST-ORDER PHASE-TRANSITION IS APPROACHED - AN EXACT TRANSFER-MATRIX STUDY

As a second-order phase transition is traversed critical scattering ap pears; these fluctuations serve notice of the impending loss of stabil ity of the equilibrium phase. For a model first-order phase transition we rigorously prove, using exact thermodynamic quantities obtained fr om 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 t he future product phase occurs. To be specific, we study the probabili ty of occupation of the product phase (stable below the transition tem perature), and demonstrate that this is a monotonically decreasing fun ction as the transition temperature is approached from above. The rela tion of this pedagogical result to x-ray scattering experiments is dis cussed.