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