Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd. / Hansen, Ulrik Thinggaard; Klausen, Frederik Ravn.

In: Journal of Mathematical Physics, Vol. 64, No. 1, 013302, 2023.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Hansen, UT & Klausen, FR 2023, 'Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd', Journal of Mathematical Physics, vol. 64, no. 1, 013302. https://doi.org/10.1063/5.0105283

APA

Hansen, U. T., & Klausen, F. R. (2023). Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd. Journal of Mathematical Physics, 64(1), [013302]. https://doi.org/10.1063/5.0105283

Vancouver

Hansen UT, Klausen FR. Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd. Journal of Mathematical Physics. 2023;64(1). 013302. https://doi.org/10.1063/5.0105283

Author

Hansen, Ulrik Thinggaard ; Klausen, Frederik Ravn. / Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd. In: Journal of Mathematical Physics. 2023 ; Vol. 64, No. 1.

Bibtex

@article{53b46285212b495596c79d9ccfb7f8bb,
title = "Strict monotonicity, continuity, and bounds on the Kert{\'e}sz line for the random-cluster model on Zd",
abstract = "Ising and Potts models can be studied using the Fortuin-Kasteleyn representation through the Edwards-Sokal coupling. This adapts to the setting where the models are exposed to an external field of strength h > 0. In this representation, which is also known as the random-cluster model, the Kert{\'e}sz line is the curve that separates two regions of the parameter space defined according to the existence of an infinite cluster in Zd. This signifies a geometric phase transition between the ordered and disordered phases even in cases where a thermodynamic phase transition does not occur. In this article, we prove strict monotonicity and continuity of the Kert{\'e}sz line. Furthermore, we give new rigorous bounds that are asymptotically correct in the limit h → 0 complementing the bounds from the work of Ruiz and Wouts [J. Math. Phys. 49, 053303 (2008)], which were asymptotically correct for h → ∞. Finally, using a cluster expansion, we investigate the continuity of the Kert{\'e}sz line phase transition. ",
author = "Hansen, {Ulrik Thinggaard} and Klausen, {Frederik Ravn}",
note = "Publisher Copyright: {\textcopyright} 2023 Author(s).",
year = "2023",
doi = "10.1063/5.0105283",
language = "English",
volume = "64",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "A I P Publishing LLC",
number = "1",

}

RIS

TY - JOUR

T1 - Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Zd

AU - Hansen, Ulrik Thinggaard

AU - Klausen, Frederik Ravn

N1 - Publisher Copyright: © 2023 Author(s).

PY - 2023

Y1 - 2023

N2 - Ising and Potts models can be studied using the Fortuin-Kasteleyn representation through the Edwards-Sokal coupling. This adapts to the setting where the models are exposed to an external field of strength h > 0. In this representation, which is also known as the random-cluster model, the Kertész line is the curve that separates two regions of the parameter space defined according to the existence of an infinite cluster in Zd. This signifies a geometric phase transition between the ordered and disordered phases even in cases where a thermodynamic phase transition does not occur. In this article, we prove strict monotonicity and continuity of the Kertész line. Furthermore, we give new rigorous bounds that are asymptotically correct in the limit h → 0 complementing the bounds from the work of Ruiz and Wouts [J. Math. Phys. 49, 053303 (2008)], which were asymptotically correct for h → ∞. Finally, using a cluster expansion, we investigate the continuity of the Kertész line phase transition.

AB - Ising and Potts models can be studied using the Fortuin-Kasteleyn representation through the Edwards-Sokal coupling. This adapts to the setting where the models are exposed to an external field of strength h > 0. In this representation, which is also known as the random-cluster model, the Kertész line is the curve that separates two regions of the parameter space defined according to the existence of an infinite cluster in Zd. This signifies a geometric phase transition between the ordered and disordered phases even in cases where a thermodynamic phase transition does not occur. In this article, we prove strict monotonicity and continuity of the Kertész line. Furthermore, we give new rigorous bounds that are asymptotically correct in the limit h → 0 complementing the bounds from the work of Ruiz and Wouts [J. Math. Phys. 49, 053303 (2008)], which were asymptotically correct for h → ∞. Finally, using a cluster expansion, we investigate the continuity of the Kertész line phase transition.

UR - http://www.scopus.com/inward/record.url?scp=85146450616&partnerID=8YFLogxK

U2 - 10.1063/5.0105283

DO - 10.1063/5.0105283

M3 - Journal article

AN - SCOPUS:85146450616

VL - 64

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 1

M1 - 013302

ER -

ID: 334252618