Mean field theory of the H^(0|2l) model on the complete graph

In this talk, we present a method for calculating the partition function of the H^{0|2l} sigma model on the complete graph K_N in the limit N \to \infty. We begin with a brief introduction to spin models on the complete graph, followed by a discussion about the l=1 case and its combinatorial analogue. We then introduce explain how the partition function can be represented in the formalism of Berezin integrals. We will then investigate the stable roots of the free energy and conclude that the H^{0|2l}-model undergoes a single phase transition. After that, we will describe the techniques used to study the model in different temperature regimes: supercritical, subcritical, and at the critical temperature, with a focus on super-critical regime.