An efficient cluster algorithm for the Ising model in an external field

We describe an extension of the Wolff algorithm that works efficiently in the presence of an external magnetic field. Local simulations of the Ising model near its continuous phase transition suffer from critical slowing-down, a power-law increase of the correlation time as the transition is approached. In the absence of an external magnetic field, this has been largely alleviated by cluster algorithms—like the Wolff algorithm—which quickly sample different highly-correlated configurations by flipping large clusters whose size scales with the correlation length. However, existing extensions of these algorithms still suffer from critical slowing-down as the transition is approached with nonzero field, e.g., along the critical isotherm. Our algorithm works in the presence of a field and extends the critical scaling of correlation time the Wolff algorithm achieves at zero field over the entire temperature–field parameter space. As an application, we directly measure observables in the metastable state of the two-dimensional Ising model in the vicinity of its critical point and show that they are described by the scaling theory of the stable state.