Vortex characterisation of frustration in the 2d Ising spin glass

The frustrated Ising model on a two-dimensional lattice with open boundary conditions is revisited. A hidden Z2 gauge symmetry relates models with different frustrations which, however, share the same partition function. By means of a duality transformation, it is shown that the partition function only depends on the distribution of gauge invariant vortices on the lattice. We finally show that the exact ground state energy can be calculated in polynomial time using Edmonds’ algorithm.