Free Energy, Gibbs Measures, and Glauber Dynamics for Nearest-neighbor Interactions on Trees Article Swipe
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Christopher Shriver
·
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2011.00653
· OA: W3096303671
YOU?
·
· 2020
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2011.00653
· OA: W3096303671
We extend results of R. Holley beyond the integer lattice to a large class of groups which includes free groups. In particular we show that a shift-invariant measure is Gibbs if and only if it is Glauber-invariant. Moreover, any shift-invariant measure converges weakly to the set of Gibbs measures when evolved under Glauber dynamics. These results are proven using a new notion of free energy density relative to a sofic approximation by homomorphisms. Any measure which minimizes free energy density is Gibbs.
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