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A simple fluctuation lower bound for a disordered
massless random continuous spin model in d=2
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Christof Kuelske, University of Groningen
Enza Orlandi, Universita di Roma Tre
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Abstract
We prove a finite volume lower bound of the order square root of log N on the delocalization of a disordered continuous spin model (resp. effective interface model) in d=2 in a box of size N.
The interaction is assumed to be massless, possibly anharmonic and dominated from above by a
Gaussian. Disorder is entering via a linear source term. For this model delocalization with the same rate is proved to take place already without disorder. We provide a bound that is
uniform in the configuration of the disorder, and so our proof shows that disorder will only enhance fluctuations.
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Full text: PDF
Pages: 200-205
Published on: September 14, 2006
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Bibliography
-
M. Aizenman and J. Wehr.
Rounding effects on quenched randomness
on first-order phase transitions. Commun. Math. Phys. 130, 489--528, 1990.
1060388
-
A. Bovier and C. Külske.
There are no nice interfaces in (2 + 1)-dimensional
SOS models in random media. J. Statist. Phys. 83, 751--759, 1996.
1386357
-
H. J. Brascamp and E. H. Lieb.
On extensions of the Brunn-Minkowski and
Prekopa-Leindler theorems, including inequalities for log concave functions,
and with an application to the diffusion equation.
J. Functional Analysis
22 366--389, 1976.
0450480
-
J. Bricmont, A. El Mellouki, and J. Fröhlich.
Random surfaces in statistical mechanics: roughening, rounding, wetting,...
J. Statist. Phys. 42, 743--798, 1986.
0833220
-
D.Ioffe, S.Shlosman, and Y. Velenik. 2D models of statistical physics with continuous
symmetry: the case of singular interactions.
Comm. Math. Phys. 226 no. 2, 433--454, 2002.
1892461
-
C. Külske. The continuous-spin random field model:
Ferromagnetic ordering in d greater or equal than three.
Rev.Math.Phys. 11,
1269--1314, 1999.
1734714
-
G. F. Lawler.
Intersections of random walks.
Basel-Boston Birkhauser, 1991.
1117680
-
C. E. Pfister. On the symmetry of the Gibbs states in two-dimensional
lattice systems. Comm. Math. Phys. 79, no.~2, 181--188, 1981.
0612247
-
Y. Velenik.
Localization and delocalization of random interfaces,
Probability Surveys 3, 112-169, 2006.
2216964
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Electronic Communications in Probability. ISSN: 1083-589X |
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