Even though the Ising model is a model of discrete variables, it is still possible to apply HMC to perform global updates, as we explain in https://arxiv.org/ab

Even though the Ising model is a model of discrete variables, it is still possible to apply HMC to perform global updates, as we explain in https://arxiv.org/abs/1912.03278 https://arxiv.org/abs/1912.03278 However, without further improvement, HMC’s performance is similar to the ‘obvious’ algorithms and poor compared to the Swendsen-Wang or Wolff cluster algorithms or the worm algorithm of Prokof’ev and Svistunov near criticality.