Abstract
A study is reported of the phase transitions in n-component abelian Higgs models, of euclidean dimensionality d = 4 − ϵ. The occurrence of a fluctuation-induced first-order transition for appropriate values of n and of the coupling constants is confirmed by explicit construction of the coexistence curve and the equation of state, at order ϵ. An exponentiation of the equation of state is obtained which: (i) is analytic in n away from thermodynamic singularities; (ii) describes either a first-order or a continuous transition depending on the value of n; (iii) incorporates canonical singularities induced by Goldstone modes on the coexistence curve, and by gauge field fluctuations in the disordered phase.
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