Thermodynamic Quantities of Magnetic Chains –Padé Approximants to High-Temperature Expansions on the Internal Energy Plane and a Polynomial Fitting

Abstract

An improved Padé method is applied to the entropy and the reduced susceptibility χ R (=χ· k B T / N ( g µ) 2 ) expanded in powers of the internal energy in order to calculate the specific heat c ( T ) for S ≤2 and the zero-field susceptibility for S =1/2 of a quantum Heisenberg spin chain, respectively. The exponents α( c ( T )∼ T α ) obtained for an antiferromagnetic exchange and 1≤ S ≤2 are 1.6, 1.4 and 1.3, which are much different from the value (α=1) given by the spin-wave theory (SW). It is also shown that the polynomials with exponents given by SW cannot fit in with the Padé approximants for these cases. This disagreement with the behaviors of SW is ascribed, at least for S =1, to the nonzero gap found by Botet and Jullien.