Finite size effects in the phase transition patterns of coupled scalar field systems

Abstract

It is considered in this work the phase transition patterns for a coupled two-scalar field system model under the combined effects of finite sizes and temperature. The scalar fields are taken as propagating in a $D=4$ Euclidean space with the usual periodic compactification in the Euclidean time direction (with dimension given by the inverse of the temperature) and also under a compact dimension in the space direction, which is restricted to size $L$. In the latter case, a Dirichlet boundary condition is considered. Finite-size variation of the critical temperature for the cases of symmetry restoration and inverse symmetry breaking are studied. At fixed finite-temperature values, the variation of the inverse correlation lengths with the size $L$ might display a behavior analogous to reentrant phase transitions. Possible applications of our results to physical systems of interest are also discussed.