Accelerating hybrid stochastic algorithm for spin models

The problem of critical slowing down in simulations of statistical mechanics systems is discussed in the context of hybrid stochastic differential equations. By modifying the kinetic energy part of the system's molecular dynamics lagrangian, new algorithms are presented which evolve the system's infra-red modes as rapidly as their ultraviolet ones. These improved (“accelerated”) algorithms should yield accurate measurements of the critical behavior of models of magnets, glasses, etc. which have not been practical in the past.