  A quasi two-dimensional non-relativistic 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 to
the one-loop correction is discussed in the context of condensed matter theory
where it is referred to as the Thouless criterion for superconductivity. By
reference to the appropriate modified effective potential one may revise the
Thouless criterion to obtain a critical temperature in next-to-leading order
that, unlike the mean-field temperature, tends to zero in the two-dimensional
limit in agreement with the Coleman theorem.
