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We compute the free energy in the presence of a chemical potential coupled toa conserved charge in the effective SU(N)xSU(N) scalar field theory to thirdorder for asymmetric volumes in general d-dimensions, using dimensionalregularization. We also compute the mass gap in a finite box with periodicboundary conditions.

Finite volume mass gap and free energy of the SU(N)xSU(N) chiral sigma model