Abstract
Catastrophe theory predicts that in certain limits universal relations should exist between barrier heights, curvatures and the positions of local maxima and minima on a potential or free energy surface. In the present work we investigate these relations for both first- and second-order phase transitions, revealing that the ideal ratios often hold quite well over a wide range of conditions. This elementary catastrophe theory is illustrated for the melting transition of an atomic cluster, the isotropic-to-nematic transition in a liquid crystal, and the ferromagnetic-to-paramagnetic phase transition in the two-dimensional Ising model.
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