On the series expansion of the general spin- S Ising chain

Abstract

Thermodynamical properties of spin- S Ising chains can nowadays be easily obtained using numerical calculation. However, from a mathematical point of view, its exact solution for arbitrary spin is still a challenge. Only limiting cases have been solved exactly, such as the infinite spin limit and lowest spin values. The present article addresses this issue. Using the high-temperature series expansion we obtain a new analytical series expansion of the partition function for the Ising chain, in the absence of magnetic field. Our general results cover all spins from 1 2 to infinite, in the high-temperature region, up to order β 40 ( β = ( kT ) - 1 ) . In order to extend our results to finite-temperature we employ the method presented in the work of Ref. [Bernu and Misguich, Phys. Rev. B63 (2001) 134409]. We also present a matrix formulation of our series expansion and relate it to the transfer matrix technique.