1999
DOI: 10.1007/s002200050646
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Interface, Surface Tension and Reentrant Pinning Transition in the 2D Ising Model

Abstract: We develop a new way to look at the high-temperature representation of the Ising model up to the critical temperature and obtain a number of interesting consequences. In the two-dimensional case, it is possible to use these tools to prove results on phaseseparation lines in the whole phase-coexistence regime, by way of a duality transformation. We illustrate the power of these techniques by studying an Ising model with a boundary magnetic field, in which a reentrant pinning transition takes place; more precise… Show more

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Cited by 41 publications
(91 citation statements)
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“…Equations (2.2) and (2.3) define the random-line representation for the 2-point function of the Ising model on the graph G. It has been studied in detail in [PV1,PV2] and is essentially equivalent (though the derivations are quite different) to the random-walk representation of [Az]. We'll need a version of this representation on the infinite graph (Z d , E J ).…”
Section: Renormalizationmentioning
confidence: 99%
See 2 more Smart Citations
“…Equations (2.2) and (2.3) define the random-line representation for the 2-point function of the Ising model on the graph G. It has been studied in detail in [PV1,PV2] and is essentially equivalent (though the derivations are quite different) to the random-walk representation of [Az]. We'll need a version of this representation on the infinite graph (Z d , E J ).…”
Section: Renormalizationmentioning
confidence: 99%
“…We'll need a version of this representation on the infinite graph (Z d , E J ). To this end, we use the following result ([PV2], Lemmas 6.3 and 6.9): For all β < β c ,…”
Section: Renormalizationmentioning
confidence: 99%
See 1 more Smart Citation
“…• ( [27], Lemma 6.3) The limiting weights q * β * ,h * = lim E↑E * q * β * ,h * ,E and q * β * ,h * ,s.i. = lim E↑E * s.i.…”
Section: A Some Toolsmentioning
confidence: 99%
“…• ( [27], Lemma 6.4) If γ = γ 1 ∐ γ 2 (∐ is a concatenation operation, see [27] for a definition), then q * β * ,h * ,E (γ) ≥ q * β * ,h * ,E (γ 1 ) q * β * ,h * ,E (γ 2 • ( [29], Lemma 4.4.6, and [27], Lemma 6.10) Let R be a rectangular subset of E * having length R 2 /(K log R) and height R, with basis contained inside {e * = x, y ∈ E * : x 2 = y = 2 = 1/2}. We denote by u and v the dual sites at the bottom left and bottom right corners of R. Then, for K large enough, there exists C < ∞ such that where · β * ,h * and · β * ,h * ,s.i.…”
Section: A Some Toolsmentioning
confidence: 99%