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

共 50 条

[1] Entanglement gap in 1D long-range quantum spherical models
Wald, Sascha
Arias, Raul
Alba, Vincenzo
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2023, 56 (24)
[2] Heat conduction and long-range spatial correlation in 1D models
Xin, Z
Iwamoto, M
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (46): : 11123 - 11133
[3] Long-range interactions in 1D heterogeneous solids with uncertainty
Muscolino, G.
Sofi, A.
Zingales, M.
IUTAM SYMPOSIUM ON MULTISCALE PROBLEMS IN STOCHASTIC MECHANICS, 2013, 6 : 69 - 78
[4] Lyapunov Exponents in 1D Anderson Localization with Long-range Correlations
Iomin, Alexander
JOURNAL OF SIBERIAN FEDERAL UNIVERSITY-MATHEMATICS & PHYSICS, 2010, 3 (03): : 297 - 302
[5] Delocalization in the 1D Anderson model with long-range correlated disorder
de Moura, FABF
Lyra, ML
PHYSICAL REVIEW LETTERS, 1998, 81 (17) : 3735 - 3738
[6] Universality in the time correlations of the long-range 1d Ising model
Corberi, Federico
Lippiello, Eugenio
Politi, Paolo
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2019,
[7] Comment on "Delocalization in the 1D Anderson model with long-range correlated disorder"
Kantelhardt, JW
Russ, S
Bunde, A
Havlin, S
Webman, I
PHYSICAL REVIEW LETTERS, 2000, 84 (01) : 198 - 198
[8] Long-range memory elementary 1D cellular automata: Dynamics and nonextensivity
Rohlf, Thimo
Tsallis, Constantino
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2007, 379 (02) : 465 - 470
[9] Short-time dynamics in the 1D long-range Potts model
K. Uzelac
Z. Glumac
O. S. Barišić
The European Physical Journal B, 2008, 63 : 101 - 108
[10] Loss of Stability in a 1D Spin Model with a Long-Range Random Hamiltonian
Littin, Jorge
Maldonado, Cesar
JOURNAL OF STATISTICAL PHYSICS, 2023, 191 (01)

← 1 2 3 4 5 →