Abstract
Non-Fellerian particle systems are characterized by nonlocal interactions, somewhat analogous to non-Gibbsian distributions. They exhibit new phenomena that are unseen in standard interacting particle systems. We consider freezing transitions in one-dimensional non-Fellerian processes which are built from the abelian sandpile additions to which in one case, spin flips are added, and in another case, so called anti-sandpile subtractions. In the first case and as a function of the sandpile addition rate, there is a sharp transition from a non-trivial invariant measure to the trivial invariant measure of the sandpile process. For the combination sandpile plus anti-sandpile, there is a sharp transition from one frozen state to the other anti-state.
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Maes, C., Redig, F. & Saada, E. Freezing Transitions in Non-Fellerian Particle Systems. J Stat Phys 127, 171–189 (2007). https://doi.org/10.1007/s10955-007-9279-z
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DOI: https://doi.org/10.1007/s10955-007-9279-z