Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 59, Number 1 (2015), 143-187.
Long range correlation inequalities for massless Euclidean fields
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.
Illinois J. Math., Volume 59, Number 1 (2015), 143-187.
Received: 7 April 2015
Revised: 26 August 2015
First available in Project Euclid: 11 February 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs 82B28: Renormalization group methods [See also 81T17]
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