科研之友
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摘要
We consider the standard site percolation model on the d-dimensional lattice. A direct consequence of the proof of the uniqueness of the infinite cluster of Aizenman, Kesten and Newman [Comm. Math. Phys. 111 (1987) 505-531] is that the two-arms exponent is larger than or equal to 1/2. We improve slightly this lower bound in any dimension d >= 2. Next, starting only with the hypothesis that theta(p) > 0, without using the slab technology, we derive a quantitative estimate establishing long-range order in a finite box.
- 出版日期2015-9
