Gibbs-non-Gibbs properties for n-vector lattice and mean-field models

Aernout C. D. van Enter; Christof Kulske; Alex A. Opoku; Wioletta M. Ruszel

doi:10.1214/09-BJPS029

Gibbs-non-Gibbs properties for n-vector lattice and mean-field models

Aernout C. D. van Enter^*, Christof Kulske, Alex A. Opoku, Wioletta M. Ruszel

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

We review some recent developments in the study of Gibbs and non-Gibbs properties of transformed n-vector lattice and mean-field models under various transformations. Also, some new results for the loss and recovery of the Gibbs property of planar rotor models during stochastic time evolution are presented.

Original language	English
Pages (from-to)	226-255
Number of pages	30
Journal	Brazilian journal of probability and statistics
Volume	24
Issue number	2
DOIs	https://doi.org/10.1214/09-BJPS029
Publication status	Published - Jul-2010

Keywords

Gibbs measures
non-Gibbsian measures
n-vector lattice models
n-vector mean-field models
transformed model
Dobrushin uniqueness
cluster expansion
spin-flop transitions
RENORMALIZATION-GROUP TRANSFORMATIONS
FUZZY POTTS-MODEL
GIBBSIANNESS
REGULARITY
RECOVERY
SYMMETRY
SYSTEMS

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@article{8965612e3bf34e91b2c491e306f71db4,

title = "Gibbs-non-Gibbs properties for n-vector lattice and mean-field models",

abstract = "We review some recent developments in the study of Gibbs and non-Gibbs properties of transformed n-vector lattice and mean-field models under various transformations. Also, some new results for the loss and recovery of the Gibbs property of planar rotor models during stochastic time evolution are presented.",

keywords = "Gibbs measures, non-Gibbsian measures, n-vector lattice models, n-vector mean-field models, transformed model, Dobrushin uniqueness, cluster expansion, spin-flop transitions, RENORMALIZATION-GROUP TRANSFORMATIONS, FUZZY POTTS-MODEL, GIBBSIANNESS, REGULARITY, RECOVERY, SYMMETRY, SYSTEMS",

author = "{van Enter}, {Aernout C. D.} and Christof Kulske and Opoku, {Alex A.} and Ruszel, {Wioletta M.}",

year = "2010",

month = jul,

doi = "10.1214/09-BJPS029",

language = "English",

volume = "24",

pages = "226--255",

journal = "Brazilian journal of probability and statistics",

issn = "0103-0752",

number = "2",

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TY - JOUR

T1 - Gibbs-non-Gibbs properties for n-vector lattice and mean-field models

AU - van Enter, Aernout C. D.

AU - Kulske, Christof

AU - Opoku, Alex A.

AU - Ruszel, Wioletta M.

PY - 2010/7

Y1 - 2010/7

N2 - We review some recent developments in the study of Gibbs and non-Gibbs properties of transformed n-vector lattice and mean-field models under various transformations. Also, some new results for the loss and recovery of the Gibbs property of planar rotor models during stochastic time evolution are presented.

AB - We review some recent developments in the study of Gibbs and non-Gibbs properties of transformed n-vector lattice and mean-field models under various transformations. Also, some new results for the loss and recovery of the Gibbs property of planar rotor models during stochastic time evolution are presented.

KW - Gibbs measures

KW - non-Gibbsian measures

KW - n-vector lattice models

KW - n-vector mean-field models

KW - transformed model

KW - Dobrushin uniqueness

KW - cluster expansion

KW - spin-flop transitions

KW - RENORMALIZATION-GROUP TRANSFORMATIONS

KW - FUZZY POTTS-MODEL

KW - GIBBSIANNESS

KW - REGULARITY

KW - RECOVERY

KW - SYMMETRY

KW - SYSTEMS

U2 - 10.1214/09-BJPS029

DO - 10.1214/09-BJPS029

M3 - Article

SN - 0103-0752

VL - 24

SP - 226

EP - 255

JO - Brazilian journal of probability and statistics

JF - Brazilian journal of probability and statistics

IS - 2

ER -

Gibbs-non-Gibbs properties for n-vector lattice and mean-field models

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Keywords

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