Potts models with a defect line

Abstract

We provide a detailed analysis of the correlation length in the direction parallel to a line of modified coupling constants in the ferromagnetic Potts model on ${\mathbb{Z}}^d$ at temperatures $T>T_c$. We also describe how a line of weakened bonds pins the interface of the Potts model on ${\mathbb{Z}}^2$ below its critical temperature. These results are obtained by extending the analysis by Friedli, Ioffe and Velenik from Bernoulli percolation to FK-percolation of arbitrary parameter $q>1$.

Final version, as accepted for publication in Communications in Mathematical Physics. (Includes a few improvements in the presentation compared with the previous version.)

References in corpus (3)

• Localization and delocalization of random interfaces
• Fluctuation theory of connectivities for subcritical random cluster models
• Interface localization near criticality

Cited by in corpus (9)

• Critical prewetting in the 2d Ising model
• Asymptotics of even-even correlations in the Ising model
• Sharp Asymptotics for the Truncated Two-Point Function of the Ising Model with a Positive Field
• Invariance principle for a Potts interface along a wall
• Non-analyticity of the correlation length in systems with exponentially decaying interactions
• On the two-point function of the Potts model in the saturation regime
• On level line fluctuations of SOS surfaces above a wall
• Ornstein-Zernike behavior for Ising models with infinite-range interactions
• Entropic repulsion and scaling limit for a finite number of non-intersecting subcritical FK interfaces