The Spectral Gap of the 2-D Stochastic Ising Model with Mixed Boundary Conditions
The Spectral Gap of the 2-D Stochastic Ising Model with Mixed Boundary Conditions
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DOI：
10.1023/a:1010382316368
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发表时间：
2000-08
影响因子：
1.6
通讯作者：
K. S. Alexander;N. Yoshida
中科院分区：
文献类型：
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作者：
K. S. Alexander;N. Yoshida
我们建立了随机伊辛模型在低温下的谱隙的上界，在一个n-by-n盒子中，边界条件不是纯粹的正或负;具体地说，我们假设边界中每个长度为n的区间上的边界自旋之和的大小由下式限定： n，其中< 1。我们表明，对于任何这样的边界条件，当温度足够低（取决于），光谱间隙呈指数下降n。
We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an n-by-n box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length n in the boundary is bounded by n, where < 1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on ), the spectral gap decreases exponentially in n.