One-dimensional Ising model with multispin interactions

Loïc Turban (1)

1 IJL - Institut Jean Lamour

We study the spin-1/2 Ising chain with multispin interactions K involving the product of m successive spins, for general values of m. Using a change of spin variables the zero-field partition function of a finite chain is obtained for free and periodic boundary conditions (BC) and we calculate the two-spin correlation function. When placed in an external field H the system is shown to be self-dual. Using another change of spin variables the one-dimensional (1D) Ising model with multispin interactions in a field is mapped onto a zero-field rectangular Ising model with first-neighbour interactions K and H. The 2D system, with size m×N/m, has the topology of a cylinder with helical BC. In the thermodynamic limit N/m → ∞, m → ∞, a 2D critical singularity develops on the self-duality line, sinh 2K sinh 2H = 1.

Mots clés: Ising model; multispin interaction; self-duality; helical boundary conditions

Domaines: Mécanique statistique [cond-mat.stat-mech]

Loïc Turban. One-dimensional Ising model with multispin interactions. Journal of Physics A: Mathematical and Theoretical, 2016, ⟨10.1088/1751-8113/49/35/355002⟩. ⟨hal-01352924⟩