  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 $\mu$ 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 $\cosh\mu$ or
$\sinh\mu$ 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.
