Long-range models in 1D revisited

被引：1

作者：

Duminil-Copin, Hugo ^{[1
,2
]}

Garban, Christophe ^{[3
,4
]}

Tassion, Vincent ^{[5
]}

机构：

[1] Univ Geneva, 2-4 Rue Lievre, CH-1204 Geneva, Switzerland

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

[3] Univ Claude Bernard Lyon 1, Inst Camille Jordan, CNRS UMR 5208, F-69622 Villeurbanne, France

[4] Inst Univ France IUF, Paris, France

[5] Swiss Fed Inst Technol, Dept Math, Grp 3 HG G 66-5 Ramistr 101, CH-8092 Zurich, Switzerland

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2024年 / 60卷 / 01期

基金：

欧洲研究理事会;

关键词：

Percolation; Long-range; Renormalization; Critical; One-dimension; PERCOLATION; DISCONTINUITY; MAGNETIZATION; TRANSITION; PHASE;

D O I：

10.1214/22-AIHP1355

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：

In this short note, we revisit a number of classical results on long-range 1D percolation, Ising model and Potts models (Comm. Math. Phys. 84 (1982) 87-101; Comm. Math. Phys. 104 (1986) 547-571; J. Stat. Phys. 50 (1988) 1-40; Comm. Math. Phys. 118 (1988) 303-336). More precisely, we show that for Bernoulli percolation, FK percolation and Potts models, there is symmetry breaking for the 1/r2-interaction at large 0, and that the phase transition is necessarily discontinuous. We also show, following the notation of (J. Stat. Phys. 50 (1988) 1-40) that 0*(q) = 1 for all q >= 1.

引用

页码：232 / 241

页数：10

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