Low-Temperature Long-Time Simulations of Ising Ferromagnets using the Monte Carlo with Absorbing Markov Chains method

Abstract

The Monte Carlo with Absorbing Markov Chains (MCAMC) method is introduced. This method is a generalization of the rejection-free method known as the $n$-fold way. The MCAMC algorithm is applied to the study of the very low-temperature properties of the lifetime of the metastable state of Ising ferromagnets. This is done both for square-lattice and cubic-lattice nearest-neighbor models. Comparison is made with exact low-temperature predictions, in particular the low-temperature predictions that the metastable lifetime is discontinuous at particular values of the field. This discontinuity for the square lattice is not seen in finite-temperatures studies. For the cubic lattice, it is shown that these `exact predictions' are incorrect near the fields where there are discontinuities. The low-temperature formula must be modified and the corrected low-temperature predictions are not discontinuous in the energy of the nucleating droplet.