Abstract: Onsager proposed a closed-form expression for the free energy of the 2D classical Ising model in 1944. In 1952, Kac and Ward introduced an alternative elegant method of combinatorial nature. Kager, Lis and Meester in 2013 and Aizenman and Warzel in 2018 gave a rigorous proof of the latter. We extend their result to the triangular lattice as well as with coupling constants of arbitary sign. Furthermore, we derive rigorously the free energy of the 1D quantum Ising model. This is joint work with Daniel Ueltschi.
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