A gauge invariant cluster algorithm for the Ising spin glass

The frustrated Ising model in two dimensions is revisited. The frustration is quantified in terms of the number of non-trivial plaquettes which is invariant under the Nishimori gauge symmetry. The exact ground state energy is calculated using Edmond's algorithm. A novel cluster algorithm is designed which treats gauge equivalent spin glasses on equal footing and allows for efficient simulations near criticality. As a first application, the specific heat near criticality is investigated.