Compatibility between the Ginzburg–Landau model and finite-temperature quantum field theory

Abstract

The formalism of finite-temperature quantum field theory, as developed by Matsubara, is applied to a Hamiltonian of N scalar fields with a quartic self-interaction at large N. A renormalized expression in the lowest quantum approximation is obtained for the squared mass m2 of the field, as a function of the temperature T, from which we study the process of spontaneous symmetry breaking. We find that in a range of values around the critical temperature Tc, the squared mass can be approximated by a linear relation m2 [Formula: see text] (T − Tc). We thus demonstrate the compatibility of the finite-temperature formalism for scalar fields, in the vicinity of criticality, with respect to the Ginzburg–Landau model. We also discuss the effects caused by the presence of a chemical potential and of an external magnetic field applied to the finite-temperature system, which however do not affect the linearity of the relation between the squared mass and the temperature.