Spin clusters and conformal field theory

Abstract

We study numerically the fractal dimensions and the bulk three-point connectivity for the spin clusters of the Q-state Potts model in two dimensions with $1\le Q\le 4$. We check that the usually invoked correspondence between FK clusters and spin clusters works at the level of fractal dimensions. However, the fine structure of the conformal field theories describing critical clusters first manifests at the level of the three-point connectivities. Contrary to what recently found for FK clusters, no obvious relation emerges for generic Q between the spin cluster connectivity and the structure constants obtained from analytic continuation of the minimal model ones. The numerical results strongly suggest then that spin and FK clusters are described by conformal field theories with different realizations of the color symmetry of the Potts model.

16 pages, 8 Figures, Revised version (Fig. 7 added)

References in corpus (5)

• Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator
• SLE in the three-state Potts model - a numerical study
• Parafermionic excitations and critical exponents of random cluster and O(n) models
• Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
• Field theory of Ising percolating clusters

Cited by in corpus (7)

• Two-dimensional O(n) models and logarithmic CFTs
• Local logarithmic correlators as limits of Coulomb gas integrals
• Numerical Investigations of SO(4) Emergent Extended Symmetry in Spin-1/2 Heisenberg Antiferromagnetic Chains
• Corner contribution to cluster numbers in the Potts model
• Critical points in coupled Potts models and correlated percolation
• On the CFT describing the spin clusters in 2d Potts model
• Backbone three-point correlation function in the two-dimensional Potts model