Intermediate Fluctuations in the Ising Model

被引：0

作者：

Ott, Sebastien ^{[1
]}

Shlosman, Senya ^{[2
,3
,4
]}

Velenik, Yvan ^{[5
]}

机构：

[1] Univ Fribourg, Dept Math, Fribourg, Switzerland

[2] Skolkovo Inst Sci & Technol, Moscow, Russia

[3] Univ Toulon & Var, Aix Marseille Univ, CNRS, CPT, Marseille, France

[4] RAS, Inst Informat Transmiss Problems, Moscow, Russia

[5] Univ Geneva, Sect Math, CH-1211 Geneva, Switzerland

来源：

MARKOV PROCESSES AND RELATED FIELDS | 2024年 / 30卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

Ising model; Wulf shape; Gaussian fluctuations; KPZ fluctuations;

D O I：

10.61102/1024-2953-mprf.2024.30.1.004

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 study the fluctuations of the boundary of a large droplet of one phase of the low -T 2D Ising model in a N x N box. It is known that these fluctuations are of the order of N(1/3 )in the vicinity of the walls, and of the order of N-1/2 far away from the walls. We argue that in fact the fluctuations of this interface can be of any order N-b , 1/3 <= b <= 1/2, depending on the location on the interface. We state a conjecture concerning the locations where the fluctuations are of the order N-b .

引用

页数：181

共 6 条

[1] DKS DOBRUSHIN R.L., 1992, Wulff construction: a global shape from local interaction, V104, P204
[2] Dobrushin R, 1996, PROBAB THEORY REL, V105, P423
[3] Fluctuations of the phase boundary in the 2D Ising ferromagnet
Dobrushin, R
Hryniv, O
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 189 (02) : 395 - 445
[4] CRITICAL PREWETTING IN THE 2D ISING MODEL
Ioffe, Dmitry
Ott, Sebastien
Shlosman, Senya
Velenik, Yvan
[J]. ANNALS OF PROBABILITY, 2022, 50 (03) : 1127 - 1172
[5] An Invariance Principle to Ferrari-Spohn Diffusions
Ioffe, Dmitry
Shlosman, Senya
Velenik, Yvan
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2015, 336 (02) : 905 - 932
[6] Constrained variational problem with applications to the Ising model
Schonmann, RH
Shlosman, SB
[J]. JOURNAL OF STATISTICAL PHYSICS, 1996, 83 (5-6) : 867 - 905

← 1 →