Critical Ising on the Square Lattice Mixes in Polynomial Time |
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Authors: | Eyal?Lubetzky Email author" target="_blank">Allan?SlyEmail author |
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Institution: | 1.Microsoft Research,Redmond,USA;2.Department of Statistics,UC Berkeley,Berkeley,USA |
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Abstract: | The Ising model is widely regarded as the most studied model of spin-systems in statistical physics. The focus of this paper
is its dynamic (stochastic) version, the Glauber dynamics, introduced in 1963 and by now the most popular means of sampling
the Ising measure. Intensive study throughout the last three decades has yielded a rigorous understanding of the spectral-gap
of the dynamics on everywhere except at criticality. While the critical behavior of the Ising model has long been the focus for physicists,
mathematicians have only recently developed an understanding of its critical geometry with the advent of SLE, CLE and new
tools to study conformally invariant systems. |
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Keywords: | |
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