TY - JOUR

T1 - A Short Proof of the Discontinuity of Phase Transition in the Planar Random-Cluster Model with q> 4

AU - Ray, Gourab

AU - Spinka, Yinon

N1 - Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2020/9/1

Y1 - 2020/9/1

N2 - The goal of this paper is to provide a short proof of the discontinuity of phase transition for the random-cluster model on the square lattice with parameter q> 4. This result was recently shown in Duminil-Copin et al. (arXiv:1611.09877, 2016) via the so-called Bethe ansatz for the six-vertex model. Our proof also exploits the connection to the six-vertex model, but does not rely on the Bethe ansatz. Our argument is soft (in particular, it does not rely on a computation of the correlation length) and only uses very basic properties of the random-cluster model [for example, we do not even need the Russo–Seymour–Welsh machinery developed recently in Duminil-Copin et al. (Commun Math Phys 349(1):47–107, 2017)].

AB - The goal of this paper is to provide a short proof of the discontinuity of phase transition for the random-cluster model on the square lattice with parameter q> 4. This result was recently shown in Duminil-Copin et al. (arXiv:1611.09877, 2016) via the so-called Bethe ansatz for the six-vertex model. Our proof also exploits the connection to the six-vertex model, but does not rely on the Bethe ansatz. Our argument is soft (in particular, it does not rely on a computation of the correlation length) and only uses very basic properties of the random-cluster model [for example, we do not even need the Russo–Seymour–Welsh machinery developed recently in Duminil-Copin et al. (Commun Math Phys 349(1):47–107, 2017)].

UR - http://www.scopus.com/inward/record.url?scp=85089751507&partnerID=8YFLogxK

U2 - 10.1007/s00220-020-03827-9

DO - 10.1007/s00220-020-03827-9

M3 - מאמר

AN - SCOPUS:85089751507

VL - 378

SP - 1977

EP - 1988

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -