Planar Ising magnetization field II. Properties of the critical and near-critical scaling limits

摘要

In (Ann. Probab. 43 (2015) 528-571), we proved that the renormalized critical Ising magnetization fields Phi(a) := a(15/8)Sigma(x is an element of az2)sigma(x)delta(x) converge as a -> 0 to a random distribution that we denoted by Phi(infinity). The purpose of this paper is to establish some fundamental properties satisfied by this Phi(infinity) and the near-critical fields More precisely, we obtain the following results.