## Illinois Journal of Mathematics

### Long range correlation inequalities for massless Euclidean fields

#### Abstract

In this paper, new correlation inequalities are obtained for massless Euclidean fields on the $d$ dimensional integer lattice. Some of the inequalities have been obtained previously, in the case where the Lagrangian is a very small perturbation of a quadratic, using the renormalization group method. The results of the present paper apply provided the Lagrangian is uniformly convex. They therefore hold for the Coulomb dipole gas in which particle density can be of order $1$. The approach of the present paper is based on the methodology of Naddaf–Spencer, which relates second moment correlation functions for the Euclidean field to expectations of Green’s functions for parabolic PDE with random coefficients.

#### Article information

Source
Illinois J. Math., Volume 59, Number 1 (2015), 143-187.

Dates
Revised: 26 August 2015
First available in Project Euclid: 11 February 2016

https://projecteuclid.org/euclid.ijm/1455203163

Digital Object Identifier
doi:10.1215/ijm/1455203163

Mathematical Reviews number (MathSciNet)
MR3459632

Zentralblatt MATH identifier
06549060

#### Citation

Conlon, Joseph G.; Fahim, Arash. Long range correlation inequalities for massless Euclidean fields. Illinois J. Math. 59 (2015), no. 1, 143--187. doi:10.1215/ijm/1455203163. https://projecteuclid.org/euclid.ijm/1455203163

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