One point functions in large N vector models at finite chemical potential

We evaluate the thermal one point function of higher spin currents in the critical model of U(N) complex scalars interacting with a quartic potential and the U(N) Gross-Neveu model of Dirac fermions at large N and strong coupling using the Euclidean inversion formula. These models are considered in odd space time dimensions d and held at finite temperature and finite real chemical potential μ measured in units of the temperature. We show that these one point functions simplify both at large spin and large d. At large spin, the one point functions behave as though the theory is free, the chemical potential appears through a simple pre-factor which is either cosh μ or sinh μ depending on whether the spin is even or odd. At large d, but at finite spin and chemical potential, the 1-point functions are suppressed exponentially in d compared to the free theory. We study a fixed point of the critical Gross-Neveu model in d = 3 with 1-point functions exhibiting a branch cut in the chemical potential plane. The critical exponent for the free energy or the pressure at the branch point is 3/2 which coincides with the mean field exponent of the Lee-Yang edge singularity for repulsive core interactions.