Efficient Exact Sampling for the Ising Model at all Temperatures

We present a technique that makes exact sampling of the Ising model on the square lattice at all temperatures possible in polynomial time. For this we use the results of the work that was done in the last 40 years together with the recent and seminal paper of Lubetzky and Sly that shows rapid mixing at the critical temperature. To conclude our result we need essentially the notion of duality of graphs and the Ising model on a slightly different graph.