  The Optimized Perturbation Theory (OPT) method, at finite temperature and
finite chemical potential, is applied to the field theory model for
polyacetylene. The critical dopant concentration in trans-polyacetylene is
evaluated and compared with the available experimental data and with previous
calculations. The results obtained within the OPT go beyond the standard mean
field (or large-N) approximation (MFA) by explicitly including finite N
effects. A critical analysis of the possible theoretical prescriptions to
implement and interpret these corrections to the mean field results, given the
available data, is given. For typical temperatures probed in the laboratory,
our results show that the critical dopant concentration is only weakly affected
by thermal effects.
