Thermodynamics Of Heisenberg Ferromagnet Research Articles

New insight into the thermodynamics of Heisenberg ferromagnets as inferred from high-temperature series

In search of a suitable equation of state for ferromagnets, we revise the information about the Heisenberg model obtainable from high-temperature series. Special attention is paid to the ratio χ3/χ4 (where χ⁢and⁢χ3 are the linear and cubic susceptibilities) related to Landau's quartic coefficient b. It is found in particular that both χ3/χ4 and b tend to a finite limit as T→TC. This limit is small — an order of magnitude smaller than predicted by Weiss's molecular field and similar theories — but contrary to the common belief, nonzero. This implies a rejection of the generally accepted critical-point exponents and a return to those of Landau: α=0, β=12, γ=1, etc.

A Fluctuating Field Theory for Systems of Localized Magnetic Moments

Thermodynamics of Heisenberg ferromagnets is described by means of a fluctuating exchange field operating on the atomic magnetic moments. A self-consistent method for calculating field characteristics is developed at arbitrary temperatures. It is shown that transitions in a paramagnetic state may pass both continuously and stepwise on temperature subject to magnitude of single-site susceptibility.

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 $[{(\mathrm{C}{\mathrm{H}}_{3})}_{4}\mathrm{N}\mathrm{Cu}{\mathrm{Cl}}_{3}]$, 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.