First-order phase transitions in superconducting films: A Euclidean model

Abstract

In the context of the Ginzburg-Landau theory for critical phenomena, we consider the Euclidean $\ensuremath{\lambda}{\ensuremath{\phi}}^{4}+\ensuremath{\eta}{\ensuremath{\phi}}^{6}$ model bounded by two parallel planes, a distance $L$ separating them. This is supposed to describe a sample of a superconducting material undergoing a first-order phase transition. We are able to determine the dependence of the transition temperature ${T}_{c}$ for the system as a function of $L$. We show that ${T}_{c}(L)$ is a concave function of $L$, in qualitative accordance with some experimental results. The form of this function is rather different from the corresponding one for a second-order transition.