Mixing Time for the Ising Model: a Uniform Lower Bound for All Graphs
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چکیده
Consider Glauber dynamics for the Ising model on a graph of n vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least n log n/f(∆), where ∆ is the maximum degree and f(∆) = Θ(∆ log ∆). Their result applies to more general spin systems, and in that generality, they showed that some dependence on ∆ is necessary. In this paper, we focus on the ferromagnetic Ising model and prove that the mixing time of Glauber dynamics on any n-vertex graph is at least (1/4 + o(1))n log n.
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تاریخ انتشار 2009