Publication

Continuous spin mean-field models: Limiting kernels and Gibbs properties of local transforms

Kulske, C. & Opoku, A. A., Dec-2008, In : Journal of Mathematical Physics. 49, 12, 31 p., 125215.

Research output: Contribution to journalArticleAcademicpeer-review

APA

Kulske, C., & Opoku, A. A. (2008). Continuous spin mean-field models: Limiting kernels and Gibbs properties of local transforms. Journal of Mathematical Physics, 49(12), [125215]. https://doi.org/10.1063/1.3021285

Author

Kulske, Christof ; Opoku, Alex A. / Continuous spin mean-field models : Limiting kernels and Gibbs properties of local transforms. In: Journal of Mathematical Physics. 2008 ; Vol. 49, No. 12.

Harvard

Kulske, C & Opoku, AA 2008, 'Continuous spin mean-field models: Limiting kernels and Gibbs properties of local transforms', Journal of Mathematical Physics, vol. 49, no. 12, 125215. https://doi.org/10.1063/1.3021285

Standard

Continuous spin mean-field models : Limiting kernels and Gibbs properties of local transforms. / Kulske, Christof; Opoku, Alex A.

In: Journal of Mathematical Physics, Vol. 49, No. 12, 125215, 12.2008.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Kulske C, Opoku AA. Continuous spin mean-field models: Limiting kernels and Gibbs properties of local transforms. Journal of Mathematical Physics. 2008 Dec;49(12). 125215. https://doi.org/10.1063/1.3021285


BibTeX

@article{cdf9849e0cd343018935d36f1654932a,
title = "Continuous spin mean-field models: Limiting kernels and Gibbs properties of local transforms",
abstract = "We extend the notion of Gibbsianness for mean-field systems to the setup of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of given local transition kernels. This generalizes previous case studies made for spins taking finitely many values to the first step in the direction to a general theory containing the following parts: (1) A formula for the limiting conditional probability distributions of the transformed system (it holds both in the Gibbs and in the non-Gibbs regime and invokes a minimization problem for a {"}constrained rate function{"}), (2) a criterion for Gibbsianness of the transformed system for initial Lipschitz-Hamiltonians involving concentration properties of the transition kernels, and (3) a continuity estimate for the single-site conditional distributions of the transformed system. While (2) and (3) have provable lattice counterparts, the characterization of (1) is stronger in mean field. As applications we show short-time Gibbsianness of rotator mean-field models on the (q-1)-dimensional sphere under diffusive time evolution and the preservation of Gibbsianness under local coarse graining of the initial local spin space.",
keywords = "lattice theory, phase transformations, RENORMALIZATION-GROUP TRANSFORMATIONS, GIBBSIANNESS, REGULARITY, DIFFUSION, RECOVERY, SYMMETRY",
author = "Christof Kulske and Opoku, {Alex A.}",
note = "Relation: https://www.rug.nl/informatica/organisatie/overorganisatie/iwi Rights: University of Groningen, Research Institute for Mathematics and Computing Science (IWI)",
year = "2008",
month = "12",
doi = "10.1063/1.3021285",
language = "English",
volume = "49",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "AMER INST PHYSICS",
number = "12",

}

RIS

TY - JOUR

T1 - Continuous spin mean-field models

T2 - Limiting kernels and Gibbs properties of local transforms

AU - Kulske, Christof

AU - Opoku, Alex A.

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

PY - 2008/12

Y1 - 2008/12

N2 - We extend the notion of Gibbsianness for mean-field systems to the setup of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of given local transition kernels. This generalizes previous case studies made for spins taking finitely many values to the first step in the direction to a general theory containing the following parts: (1) A formula for the limiting conditional probability distributions of the transformed system (it holds both in the Gibbs and in the non-Gibbs regime and invokes a minimization problem for a "constrained rate function"), (2) a criterion for Gibbsianness of the transformed system for initial Lipschitz-Hamiltonians involving concentration properties of the transition kernels, and (3) a continuity estimate for the single-site conditional distributions of the transformed system. While (2) and (3) have provable lattice counterparts, the characterization of (1) is stronger in mean field. As applications we show short-time Gibbsianness of rotator mean-field models on the (q-1)-dimensional sphere under diffusive time evolution and the preservation of Gibbsianness under local coarse graining of the initial local spin space.

AB - We extend the notion of Gibbsianness for mean-field systems to the setup of general (possibly continuous) local state spaces. We investigate the Gibbs properties of systems arising from an initial mean-field Gibbs measure by application of given local transition kernels. This generalizes previous case studies made for spins taking finitely many values to the first step in the direction to a general theory containing the following parts: (1) A formula for the limiting conditional probability distributions of the transformed system (it holds both in the Gibbs and in the non-Gibbs regime and invokes a minimization problem for a "constrained rate function"), (2) a criterion for Gibbsianness of the transformed system for initial Lipschitz-Hamiltonians involving concentration properties of the transition kernels, and (3) a continuity estimate for the single-site conditional distributions of the transformed system. While (2) and (3) have provable lattice counterparts, the characterization of (1) is stronger in mean field. As applications we show short-time Gibbsianness of rotator mean-field models on the (q-1)-dimensional sphere under diffusive time evolution and the preservation of Gibbsianness under local coarse graining of the initial local spin space.

KW - lattice theory

KW - phase transformations

KW - RENORMALIZATION-GROUP TRANSFORMATIONS

KW - GIBBSIANNESS

KW - REGULARITY

KW - DIFFUSION

KW - RECOVERY

KW - SYMMETRY

U2 - 10.1063/1.3021285

DO - 10.1063/1.3021285

M3 - Article

VL - 49

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

M1 - 125215

ER -

ID: 2724711