Exploring the Phase Diagram of the Onsager-Villain Model using Quantum Annealers

The Onsager-Villain model is an exactly solvable two-dimensional model with a tunable degree of frustration. The tuning parameter, $s$, interpolates between Villain's fully frustrated model and the nearest-neighbor ferromagnetic Ising model. This model exhibits a nontrivial phase diagram in the $s$-$T$ plane, where $T$ denotes the temperature. By adjusting the energy scale of the quantum annealing device, we effectively simulate various temperatures and reproduce the phase diagram using D-Wave's quantum annealing device as an approximate Boltzmann sampler. Leveraging the exact solution of the model, we benchmark the device's performance by obtaining physically relevant quantities such as magnetization, heat capacity and susceptibility.