The worm algorithm for the Ising model is rapidly mixing
  We prove rapid mixing of the Prokofiev-Svistunov (or worm) algorithm for the zero-field ferromagnetic Ising model, on all finite graphs and at all temperatures. As a corollary, we show how to rigorously construct simple and efficient approximation schemes for the Ising susceptibility and two-point correlation function. 
Andrea Collevecchio and Timothy M. Garoni and Timothy Hyndman and   Daniel Tokarev
math-ph cond-mat.stat-mech cs.DM math.CO math.MP math.PR