Proceedings of the Japan Academy, Series A, Mathematical Sciences

A remark on monotonicity for the Glauber dynamics on finite graphs

Tomoyuki Shirai

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We show that under the heat-bath Glauber dynamics for the ferromagnetic Ising model on a finite graph, the single spin expectation at a fixed time starting at the all-up configuration is not necessarily an increasing function of coupling constants.

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Proc. Japan Acad. Ser. A Math. Sci. Volume 86, Number 2 (2010), 33-37.

First available in Project Euclid: 1 February 2010

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Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 82C20: Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs

Glauber dynamics spectral gap spin expectation monotonicity conjecture


Shirai, Tomoyuki. A remark on monotonicity for the Glauber dynamics on finite graphs. Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 2, 33--37. doi:10.3792/pjaa.86.33.

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