On the Potts antiferromagnet on random graphs

Abstract

Extending a prior result of Contucci et al (Comm. Math. Phys. 2013), we determine the free energy of the Potts antiferromagnet on the Erdös-Rényi random graph at all temperatures for average degrees $d\le (2k-1)\ln k-2-k^{-1/2}$. In particular, we show that for this regime of $d$ there does not occur a phase transition.