Conformal invariance of crossing probabilities for the Ising model with free boundary conditions

被引：5

作者：

Benoist, Stephane ^{[1
]}

Duminil-Copin, Hugo ^{[2
]}

Hongler, Clement ^{[3
]}

机构：

[1] MIT, 182 Mem Dr, Cambridge, MA 02142 USA

[2] Inst Hautes Etud Sci, 35 Route Chartres, F-91440 Bures Sur Yvette, France

[3] Ecole Polytech Fed Lausanne, MA C1 643 Stn 8, CH-1015 Lausanne, Switzerland

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2016年 / 52卷 / 04期

关键词：

Ising model; Interfaces; Schramm-Loewner evolution; Phase transition; Crossing probabilities; Exploration trees; INTERFACES; UNIVERSALITY; STATISTICS;

D O I：

10.1214/15-AIHP698

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin (J. Stat. Phys. 98 (2000) 131-244). We do so by establishing the convergence of certain exploration processes towards SLE(3, -3/2, -3/2). We also construct an exploration tree for free boundary conditions, analogous to the one introduced by Sheffield (Duke Math. J. 147 (2009) 79-129).

引用

页码：1784 / 1798

页数：15

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