Chaotic Size Dependence in the Ising Model with Random Boundary Conditions

A.C.D. van Enter; I. Medved’; K. Netočný

Chaotic Size Dependence in the Ising Model with Random Boundary Conditions

A.C.D. van Enter, I. Medved’, K. Netočný

High Energy Physics

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Abstract

We study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing cubes are the plus and the minus state. For d=2 and d=3 we prove a similar result for sparse sequences of increasing cubes. This question was raised by Newman and Stein. Our results imply that the Newman-Stein metastate is concentrated on the plus and the minus state.

Original language	English
Pages (from-to)	479-508
Number of pages	31
Journal	Markov Processes and Related Fields
Volume	8
Issue number	3
Publication status	Published - 2002

Keywords

local- and central-limit theorems
contour models
metastates
random boundary conditions

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title = "Chaotic Size Dependence in the Ising Model with Random Boundary Conditions",

abstract = "We study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing cubes are the plus and the minus state. For d=2 and d=3 we prove a similar result for sparse sequences of increasing cubes. This question was raised by Newman and Stein. Our results imply that the Newman-Stein metastate is concentrated on the plus and the minus state.",

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author = "Enter, {A.C.D. van} and I. Medved{\textquoteright} and K. Neto{\v c}n{\'y}",

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T1 - Chaotic Size Dependence in the Ising Model with Random Boundary Conditions

AU - Enter, A.C.D. van

AU - Medved’, I.

AU - Netočný, K.

N1 - Relation: http://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen. Research Institute for Mathematics and Computing Science (IWI)

PY - 2002

Y1 - 2002

N2 - We study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing cubes are the plus and the minus state. For d=2 and d=3 we prove a similar result for sparse sequences of increasing cubes. This question was raised by Newman and Stein. Our results imply that the Newman-Stein metastate is concentrated on the plus and the minus state.

AB - We study the nearest-neighbour Ising model with a class of random boundary conditions, chosen from a symmetric i.i.d. distribution. We show for dimensions 4 and higher that almost surely the only limit points for a sequence of increasing cubes are the plus and the minus state. For d=2 and d=3 we prove a similar result for sparse sequences of increasing cubes. This question was raised by Newman and Stein. Our results imply that the Newman-Stein metastate is concentrated on the plus and the minus state.

KW - local- and central-limit theorems

KW - contour models

KW - metastates

KW - random boundary conditions

M3 - Article

VL - 8

SP - 479

EP - 508

JO - Markov Processes and Related Fields

JF - Markov Processes and Related Fields

SN - 1024-2953

IS - 3

ER -