Backbone three-point correlation function in the two-dimensional Potts model

doi:10.1103/hsph-48k8

Backbone three-point correlation function in the two-dimensional Potts model

2026-03-13

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Jesper Lykke Jacobsen

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Salas, Jesus

DOI：10.1103/hsph-48k8

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Abstract

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We study the three-point correlation function of the backbone in the two-dimensional Q-state Potts model using the Fortuin-Kasteleyn (FK) representation. The backbone is defined as the biconnected skeleton of an FK cluster after removing all dangling ends and bridges. To circumvent the severe critical slowing down in direct Potts simulations for large Q, we employ large-scale Monte Carlo simulations of the O(n) loop model on the hexagonal lattice, which is regarded to correspond to the Potts model with Q = n2. Using a highly efficient cluster algorithm, we compute the universal three-point amplitude ratios for the backbone (RBB) and FK clusters (RFK). Our computed RFK exhibits excellent agreement with exact conformal field theory predictions, validating the reliability of our numerical approach. In the critical regime, we find that RBB is systematically larger than RFK. Conversely, along the tricritical branch, RBB and RFK coincide within numerical accuracy, strongly suggesting that RBB = RFK holds throughout this regime. This finding mirrors the known equality of the backbone and FK cluster fractal dimensions at tricriticality, jointly indicating that both structures share the same geometric universality.

Keywords:

CONFORMAL-INVARIANCE

PHASE-TRANSITIONS

CRITICAL-BEHAVIOR

Backbone three-point correlation function in the two-dimensional Potts model

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