Archive ouverte HAL – Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus

Nina Javerzat ¹ Marco Picco ² Raoul Santachiara ¹

Nina Javerzat, Marco Picco, Raoul Santachiara. Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus. J.Stat.Mech., 2020, 2005, pp.053106. ⟨10.1088/1742-5468/ab7c5e⟩. ⟨hal-02416915⟩

In a recent paper, we considered the effects of the torus lattice topology on the two-point connectivity of Q-Potts clusters. These effects are universal and probe non-trivial structure constants of the theory. We complete here this work by considering the torus corrections to the three- and four-point connectivities. These corrections, which depend on the scale invariant ratios of the triangle and quadrilateral formed by the three and four given points, test other non-trivial structure constants. We also present results of Monte Carlo simulations in good agreement with our predictions.

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 2. LPTHE – Laboratoire de Physique Théorique et Hautes Energies