A New Proof of the Sharpness of the Phase Transition for Bernoulli Percolation and the Ising Model

作者：Duminil Copin Hugo^*; Tassion Vincent^*

来源：Communications in Mathematical Physics, 2016, 343(2): 725-745.

DOI：10.1007/s00220-015-2480-z

We provide a new proof of the sharpness of the phase transition for Bernoulli percolation and the Ising model. The proof applies to infinite-range models on arbitrary locally finite transitive infinite graphs. For Bernoulli percolation, we prove finiteness of the susceptibility in the subcritical regime beta < beta(c), and the mean-field lower bound P beta[0 <-> infinity] >= (beta -

• 出版日期2016-4