# Interface Pinning and Finite-Size Effects in the 2D Ising Model

@inproceedings{Pfister1997InterfacePA, title={Interface Pinning and Finite-Size Effects in the 2D Ising Model}, author={C. E. Pfister and Yvan Alain Velenik}, year={1997} }

We apply new techniques developed in [PV1] to the study of some surface effects in the 2D Ising model. We examine in particular the pinningdepinning transition. The results are valid for all subcritical temperatures. By duality we obtained new finite size effects on the asymptotic behaviour of the two– point correlation function above the critical temperature. The key–point of the analysis is to obtain good concentration properties of the measure defined on the random lines giving the high…

## 8 Citations

Large deviations and continuum limit in the 2D Ising model

- Mathematics
- 1997

Summary. We study the 2D Ising model in a rectangular box ΛL of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization ∑t∈ΛLσ(t) when L→∞ for…

Large deviations and continuum limit in the 2 D Ising model PFISTER

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We study the 2D Ising model in a rectangular box Λ L of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization ∑ t∈ΛL σ(t) when L→∞ for values of…

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Dobrushin (1972) showed that the interface of a 3D Ising model with minus boundary conditions above the $xy$-plane and plus below is rigid (has $O(1)$-fluctuations) at every sufficiently low…

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Contours associated to many interesting low-temperature statistical mechanics models (2D Ising model, (2+1)D SOS interface model, etc) can be described as self-interacting and self-avoiding walks on…

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- 2015

We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber…

Classical Billiards in a Magnetic Field and a Potential

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We study billiards in plane domains, with a perpendicular magnetic field and a potential. We give some results on periodic orbits, KAM tori and adiabatic invariants. We also prove the existence of…

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- Mathematics, Physics
- 2006

Many mathematical models of statistical physics in two dimensions are either known
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Rigorous probabilistic analysis of equilibrium crystal shapes

- Mathematics
- 2000

The rigorous microscopic theory of equilibrium crystal shapes has made enormous progress during the last decade. We review here the main results that have been obtained, both in two and higher…

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Summary. We study the 2D Ising model in a rectangular box ΛL of linear size O(L). We determine the exact asymptotic behaviour of the large deviations of the magnetization ∑t∈ΛLσ(t) when L→∞ for…

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