ZERO-TEMPERATURE LIMIT OF THE KAWASAKI DYNAMICS FOR THE ISING LATTICE GAS IN A LARGE TWO-DIMENSIONAL TORUS

被引：7

作者：

Gois, B. ^{[1
]}

Landim, C. ^{[1
,2
]}

机构：

[1] Inst Matematica Pura & Aplicada, BR-22460 Rio De Janeiro, Brazil

[2] Univ Rouen, CNRS, UMR 6085, F-76801 St Etienne, France

来源：

ANNALS OF PROBABILITY | 2015年 / 43卷 / 04期

关键词：

Ising model; Kawasaki dynamics; zero-temperature limit; scaling limit; adsorption; Brownian motion; INTERACTING BROWNIAN PARTICLES; CONSERVATIVE DYNAMICS; METASTABILITY; NUCLEATION;

D O I：

10.1214/14-AOP930

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 consider the Kawasaki dynamics at inverse temperature beta for the Ising lattice gas on a two-dimensional square of length 2L + 1 with periodic boundary conditions. We assume that initially the particles form a square of length n, which may increase, as well as L, with beta. We show that in a proper time scale the particles form almost always a square and that the center of mass of the square evolves as a Brownian motion when the temperature vanishes.

引用

页码：2151 / 2203

页数：53

共 50 条

[1] Dynamics of the two-dimensional directed Ising model: zero-temperature coarsening
Godreche, C.
Pleimling, M.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2015,
[2] Generalized Zero-Temperature Glauber Dynamics in a Two-Dimensional Square Lattice
Meng Qing-Kuan
Feng Dong-Tai
Gao Xu-Tuan
Mei Yu-Xue
CHINESE PHYSICS LETTERS, 2012, 29 (12)
[3] Zero-temperature dynamics of Ising models on the triangular lattice
Wu, CC
JOURNAL OF STATISTICAL PHYSICS, 2002, 106 (1-2) : 369 - 373
[4] Zero-Temperature Dynamics of Ising Models on the Triangular Lattice
C. Chris Wu
Journal of Statistical Physics, 2002, 106 : 369 - 373
[5] Clusters and recurrence in the two-dimensional zero-temperature stochastic Ising model
Camia, F
De Santis, E
Newman, CM
ANNALS OF APPLIED PROBABILITY, 2002, 12 (02): : 565 - 580
[6] Zero-temperature dynamics in the two-dimensional axial next-nearest-neighbor Ising model
Biswas, Soham
Chandra, Anjan Kumar
Sen, Parongama
PHYSICAL REVIEW E, 2008, 78 (04):
[7] Critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model on a triangular lattice
Janicevic, Sanja
Mijatovic, Svetislav
Spasojevic, Djordje
PHYSICAL REVIEW E, 2017, 95 (04)
[8] Phase transition in a two-dimensional Ising ferromagnet based on the generalized zero-temperature Glauber dynamics
孟庆宽
冯东太
高绪团
梅玉雪
Chinese Physics B, 2013, 22 (12) : 465 - 469
[9] Phase transition in a two-dimensional Ising ferromagnet based on the generalized zero-temperature Glauber dynamics
Meng Qing-Kuan
Feng Dong-Tai
Gao Xu-Tuan
Mei Yu-Xue
CHINESE PHYSICS B, 2013, 22 (12)
[10] Zero-temperature coarsening in the two-dimensional long-range Ising model
Christiansen, Henrik
Majumder, Suman
Janke, Wolfhard
PHYSICAL REVIEW E, 2021, 103 (05)

← 1 2 3 4 5 →