Appears in collection : 100 (102!) Years of the Ising Model

The multinomial Ising model on a graph $G=(V,E)$ is the Ising model on the N-fold “blow-up” $G_N$ of $G$, whose vertices are $V\times[N]$, and edges connect $(u,i)$ to $(v,j)$ iff $u$ and $v$ are adjacent. In the limit of large $N$ we find the critical temperature, phase transitions, conformal invariance properties at criticality, and limit shapes. This is joint work with Cosmin Pohoata.