Thermodynamics of Heisenberg ferromagnets with arbitrary spin in a magnetic field

The thermodynamic properties (magnetization, magnetic susceptibility, transverse and longitudinal correlation lengths, and specific heat) of one- and two-dimensional ferromagnets with arbitrary spin $S$ in a magnetic field are investigated by a second-order Green-function theory. In addition, quantum Monte Carlo simulations for $S=1∕2$ and $S=1$ are performed by using the stochastic series expansion method. Good agreement between the results of both approaches is found. The field dependence of the position of the maximum in the temperature dependence of the susceptibility fits well to a power law at low fields and to a linear increase at high fields. The maximum height decreases according to a power law in the whole field region. The longitudinal correlation length may show an anomalous temperature dependence: a minimum followed by a maximum with increasing temperature. Considering the specific heat in one dimension and at low magnetic fields, two maxima in its temperature dependence for both the $S=1∕2$ and $S=1$ ferromagnets are found. For $S>1$, only one maximum occurs, as in the two-dimensional ferromagnets. Relating the theory to experiments on the $S=1∕2$ quasi-one-dimensional copper salt TMCuC $\left[{\left(\mathrm{C}{\mathrm{H}}_3\right)}_4\mathrm{N}\mathrm{Cu}{\mathrm{Cl}}_3\right]$, a fit to the magnetization as a function of the magnetic field yields the value of the exchange energy, which is used to make predictions for the occurrence of two maxima in the temperature dependence of the specific heat.