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An introduction to the Propp-Wilson method of coupling-from-the-past for the Ising model is presented. It enables one to obtain exact samples from the equilibrium spin distribution for ferromagnetic interactions. Both uniform and random quenched magnetic fields are included. The time to couple from the past and its standard deviation are shown as functions of system size, temperature, and the field strength. The time should be an estimate of the ergodic time for the Ising system.

Introduction to the Propp-Wilson Method of Exact Sampling for the Ising Model