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The finite temperature effective potential in the 2+1 dimensionalNambu-Jona-Lasinio model is constructed up to the next to leading order in thelarge $N$ expansion, where $N$ is the number of flavors in the model. Thedistinctive feature of the analysis is an inclusion of an additional scalarfield, which allows us to circumvent the well known, and otherwise unavoidableproblem with the imaginary contribution to the effective potential. Inaccordance with the Mermin-Wagner-Coleman theorem, applied to the dimensionallyreduced subsystem of the zero Matsubara modes of the composite boson fields,the finite temperature effective potential reveals a global minimum at the zeroof the composite order parameter. This allows us to conclude that thecontinuous global symmetry of the NJL model is not broken for any arbitrarilysmall, finite temperature.Comment: 12 pages, 4 figures, REVTe

Next to leading order effective potential in the 2+1 dimensional Nambu–Jona-Lasinio model at finite temperature