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journal article

Tightness of the Ising-Kac Model on the Two-Dimensional Torus

Hairer, Martin  
•
Iberti, Massimo
May 1, 2018
JOURNAL OF STATISTICAL PHYSICS

We consider the sequence of Gibbs measures of Ising models with Kac interaction defined on a periodic two-dimensional discrete torus near criticality. Using the convergence of the Glauber dynamic proven by Mourrat and Weber (Commun Pure Appl Math 70:717-812, 2017) and a method by Tsatsoulis and Weber employed in we show tightness for the sequence of Gibbs measures of the Ising-Kac model near criticality and characterise the law of the limit as the measure on the torus. Our result is very similar to the one obtained by Cassandro et al. (J Stat Phys 78(3):1131-1138, 1995) on , but our strategy takes advantage of the dynamic, instead of correlation inequalities. In particular, our result covers the whole critical regime and does not require the large temperature/large mass/small coupling assumption present in earlier results.

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Type
journal article
DOI
10.1007/s10955-018-2033-x
Web of Science ID

WOS:000430731600004

Author(s)
Hairer, Martin  
Iberti, Massimo
Date Issued

2018-05-01

Publisher

SPRINGER

Published in
JOURNAL OF STATISTICAL PHYSICS
Volume

171

Issue

4

Start page

632

End page

655

Subjects

VAN

•

Kac potential

•

Ising model

•

Stochastic quantization

•

Glauber dynamic

•

Science & Technology

•

Physical Sciences

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
PROPDE  
FunderFunding(s)Grant NumberGrant URL
Available on Infoscience
September 17, 2024
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/241155
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