One-dimensional q-state Potts model with multi-site interactions

Loic Turban (1)

1 IJL - Institut Jean Lamour

A one-dimensional (1D) q-state Potts model with N sites, m-site interaction K in a field H is studied for arbitrary values of m. Exact results for the partition function and the two-point correlation function are obtained at H = 0. The system in a field is shown to be self-dual. Using a change of Potts variables, it is mapped onto a standard 2D Potts model, with first-neighbour interactions K and H, on a cylinder with helical boundary conditions (BC). The 2D system has a length N/m and a transverse size m. Thus the Potts chain with multi-site interactions is expected to develop a 2D critical singularity along the self-duality line, (e qK − 1)(e qH − 1) = q, when N/m → ∞ and m → ∞.

Mots clés: Potts model; multi-site interactions; self-duality; helical boundary conditions

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique mathématique [math-ph]

Loic Turban. One-dimensional q-state Potts model with multi-site interactions. Journal of Physics A: Mathematical and Theoretical, 2017, 50, pp.205001 - 205001. ⟨10.1088/1751-8121/aa6ad1⟩. ⟨hal-01511884⟩