Entropic repulsion of the lattice free field,II. The 0-boundary case |
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Authors: | Jean-Dominique Deuschel |
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Institution: | (1) Fachbereich Mathematik, Technische Universität Berlin, D-10623 Berlin, Germany |
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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
d
,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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Keywords: | |
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