Thermodynamics of magnetic chains withS≤52

Abstract

The specific heat $C$ and entropy $\eta$ in zero field are calculated for infinite chains of spins, coupled by a nearest-neighbor Heisenberg exchange. The data presented include all spin values $S\le \frac{5}{2}$ and cover ferromagnetic and antiferromagnetic exchange. Several techniques are used to obtain reliable estimates for the infinite chains, and much attention is given to the theory underlying these techniques. For high temperatures the series expansion of $C$ is used for the estimates. Coefficients in the series are obtained from the energy spectra of different finite chains. This method is fully described, and attention is given to the estimation of further coefficients. For intermediate temperatures, around the region where $C$ displays the characteristic broad maximum, the series expansions fail and here the estimates of the infinite chain are obtained from a suitable extrapolation of the data for finite chains. This method is shown to be correct for sufficiently high temperatures. It is applicable to a wide temperature range. For temperatures near $T=0\mathrm{}$, $C$ is described by a polynomial based on the spin-wave theory. The coefficients in this polynomial are equated such that a smooth fit in with the intermediate temperature specific heat is obtained and that at the same time the over-all entropy gain is correct. The results are, as far as possible, tabulated.