The Coleman–Weinberg effective potential in superconductivity theory

A quasi-two-dimensional nonrelativistic four-Fermi theory is studied at finite temperatures in the next-to-leading-order approximation using the Coleman–Weinberg effective potential. The appearance of an imaginary part in the one-loop correction is discussed in the context of condensed matter theory where it is called the Thouless criterion for superconductivity. By reference to the appropriate modified effective potential, the Thouless criterion can be revised to obtain a critical temperature in the next-to-leading order that, unlike the mean-field temperature, tends to zero in the two-dimensional limit in agreement with the Coleman theorem.