A geometric Monte Carlo algorithm for the antiferromagnetic Ising model with “topological” term at θ=πθ=π

In this work we study the two and three-dimensional antiferromagnetic Ising model with an imaginary magnetic field iθ   at θ=πθ=π. In order to perform numerical simulations of the system we introduce a new geometric algorithm not affected by the sign problem. Our results for the 2D model are in agreement with the analytical solution. We also present new results for the 3D model which are qualitatively in agreement with mean-field predictions.