We study the Kertész line of the -state Potts model at (inverse) temperature in the presence of an external magnetic field . This line separates the two regions of the phase diagram according to the existence or not of an infinite cluster in the Fortuin–Kasteleyn representation of the model. It is known that the Kertész line coincides with the line of first order phase transition for small fields when is large enough. Here, we prove that the first order phase transition implies a jump in the density of the infinite cluster; hence, the Kertész line remains below the line of first order phase transition. We also analyze the region of large fields and prove, using techniques of stochastic comparisons, that equals to the leading order, as goes to , where is the threshold for bond percolation.
Skip Nav Destination
Article navigation
Research Article|
May 15 2008
On the Kertész line: Some rigorous bounds
Jean Ruiz;
Jean Ruiz
a)
1Centre de Physique Théorique,
CNRS Luminy Case 907
, F-13288 Marseille Cedex 9, France
Search for other works by this author on:
Marc Wouts
Marc Wouts
b)
2Modal’X,
Université Paris Ouest-Nanterre La Défense. Bâtiment G, 200 Avenue de la République
, 92001 Nanterre Cedex, France
Search for other works by this author on:
J. Math. Phys. 49, 053303 (2008)
Article history
Received:
April 07 2008
Accepted:
April 19 2008
Citation
Jean Ruiz, Marc Wouts; On the Kertész line: Some rigorous bounds. J. Math. Phys. 1 May 2008; 49 (5): 053303. https://doi.org/10.1063/1.2924322
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Pay-Per-View Access
$40.00
Citing articles via
Almost synchronous quantum correlations
Thomas Vidick
Derivation of the Maxwell–Schrödinger equations: A note on the infrared sector of the radiation field
Marco Falconi, Nikolai Leopold
Casimir energy of hyperbolic orbifolds with conical singularities
Ksenia Fedosova, Julie Rowlett, et al.
Related Content
Strict monotonicity, continuity, and bounds on the Kertész line for the random-cluster model on Z d
J. Math. Phys. (January 2023)
The Development of Cluster and Histogram Methods
AIP Conference Proceedings (November 2003)
No replica symmetry breaking phase in the random field Ginzburg-Landau model
J. Math. Phys. (August 2019)
On the extension of the FKG inequality to n functions
J. Math. Phys. (April 2022)
Absence of replica symmetry breaking in disordered FKG-Ising models under uniform field
J. Math. Phys. (July 2020)