Abstract
This paper is a continuation of [5]. We consider the Euclidean massless free field on a boxV N of volumeN d with O-boundary condition; that is the centered Gaussian field with covariances given by the Green function of the simple random walk on ℤd,d≧3, killed as it exitsV N . We show that the probability, that all the spins are positive in the boxV N decays exponentially at a surface rateN d−1. This is in contrast with the rateN d−2 logN for the infinite field of [5].
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Communicated by J.L. Lebowitz
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Deuschel, JD. Entropic repulsion of the lattice free field, II. The 0-boundary case. Commun.Math. Phys. 181, 647–665 (1996). https://doi.org/10.1007/BF02101291
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DOI: https://doi.org/10.1007/BF02101291