Semiclassical approach to the thermodynamics of spin chains

Using the semiclassical method called pure-quantum self-consistent harmonic approximation (PQSCHA), we evaluate thermodynamic quantities of one-dimensional Heisenberg ferromagnets and antiferromagnets. Since the PQSCHA reduces their evaluation to classical-like calculations, we take advantage of Fisher’s exact solution [M. E. Fisher, Am J. Phys. 32, 343 (1964)] to get all results in an almost fully analytical way. Explicitly considered here are the specific heat, the correlation length, and the susceptibility. Good agreement with available numerical data and Monte Carlo simulations is found for $S>\mathrm{}1\mathrm{}$ ferromagnets and antiferromagnets; for the latter it is seen that topological terms and the related Haldane gap are relevant only for the lowest spin values and temperatures.