  In this article we explore a certain definition of "alternate quantization"
for the critical O(N) model. We elaborate on a prescription to evaluate the
Renyi entropy of alternately quantized critical O(N) model. We show that there
exists new saddles of the q-Renyi free energy functional corresponding to
putting certain combinations of the Kaluza-Klein modes into alternate
quantization. This leads us to an analysis of trying to determine the true
state of the theory by trying to ascertain the global minima among these saddle
points.
