A Geometric Monte Carlo Algorithm for the Antiferromagnetic Ising model with Topological Term at $theta=pi$

In this work we study the two and three-dimensional antiferromagnetic Ising model with an imaginary magnetic field $itheta$ at $theta=pi$. 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 solutions. We also present new results for the $3D$ model which are qualitatively in agreement with mean-field predictions.