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Evolution of the ABC model among the segregated configurations in the zero-temperature limit. (English. French summary) Zbl 1342.60174
Summary: We consider the ABC model on a ring in a strongly asymmetric regime. The main result asserts that the particles almost always form three pure domains (one of each species) and that this segregated shape evolves, in a proper time scale, as a Brownian motion on the circle, which may have a drift. This is, to our knowledge, the first proof of a zero-temperature limit for non-reversible dynamics whose invariant measure is not explicitly known.

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J65 Brownian motion
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
82C22 Interacting particle systems in time-dependent statistical mechanics
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