Past exam of the mathematics course of the University of Cambridge / 2017 / ia / Paper 2 / 11F / a / Solution

Use the positive exponent in the PDF. The TeX introduces a minus sign in the numerator while retaining the positive-sign normalizing constant, which would not define the stated probability distribution. The Curie–Weiss model assigns equal weights to $s$ and $-s$, since $({\sum }_j{s}_j{)}^2$ is unchanged by simultaneous reversal. This spin inversion symmetry pairs every configuration with one having the opposite value of $S_i$, so