Mixing Times of Critical Two‐Dimensional Potts Models
Mixing Times of Critical Two‐Dimensional Potts Models
复制标题
临界二维 Potts 模型的混合时间
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
E. Lubetzky
中科院分区：
文献类型：
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作者：
Reza Gheissari;E. Lubetzky
我们研究了n × n盒子上的q态Potts模型在临界βc（q）处的动力学性质。热浴Glauber动力学和团簇动力学，如Swendsen-Wang（绕过低温瓶颈）在周期性边界条件下都将经历“临界减速”：在亚临界状态下的逆谱隙为O（1），在临界状态下应为n的多项式，其中1 < q ≤ 4，并且对于q > 4，n是指数的。第二作者和Sly在q = 2（伊辛模型）时证实了这一点，Borgs等人在q足够大时也证实了这一点。
We study dynamical aspects of the q‐state Potts model on an n × n box at its critical βc(q). Heat‐bath Glauber dynamics and cluster dynamics such as Swendsen–Wang (that circumvent low‐temperature bottlenecks) are all expected to undergo “critical slowdowns” in the presence of periodic boundary conditions: the inverse spectral gap, which in the subcritical regime is O(1), should at criticality be polynomial in n for 1 < q ≤ 4, and exponential in n for q > 4 in accordance with the predicted discontinuous phase transition. This was confirmed for q = 2 (the Ising model) by the second author and Sly, and for sufficiently large q by Borgs et al.
SwendsenâWang 和 heatâbath 动力学比较
影响因子：
1
作者：
M. Ullrich
通讯作者：
M. Ullrich