Thermodynamic properties of one-dimensional magnetic systems with arbitrary spin

Samuel Sitotaw, Rostislav A. Serota

Andrei A. Zvyagin, P. Schlottmann

The one-dimensional t - J model at the supersymmetric point, J = 2t, with a magnetic impurity of arbitrary spin S is studied exactly using the Bethe ansatz technique. The impurity interacts by spin exchange with the electrons on neighbouring sites of a lattice without destroying the integrability. The discrete Bethe ansatz equations diagonalizing the model, and the thermodynamic equations are derived. The impurity free energy is obtained for arbitrary band filling as a function of temperature and external magnetic field. The impurity can localize up to one itinerant hole, and has in general mixed-valent properties.

Karol Szałowski, T. Balcerzak

In the paper the Pair Approximation (PA) method for studies of the site-diluted spin-1/2 systems of arbitrary dimensionality with the long-range ferromagnetic interactions is adopted. The method allows to take into account arbitrary anisotropy of the interactions in the spin space, so it is not limited to purely Ising couplings. Within this approach, the Gibbs free energy is obtained, which allows to derive all the further interesting thermodynamic properties. In particular, we obtain an equation for the critical temperature of the second-order phase transitions for the model in question. In the study we focus our attention on the systems with ferromagnetic interactions decaying with the distance according to the power law $J(r)\propto r^{-n}$. We discuss the dependence of the critical temperature on the concentration of magnetic component and the index $n$ for selected one-, two- and three-dimensional lattices.We confirm the absence of the critical concentration for a diluted magnet with infinite interaction range. In the regime of the low concentrations of magnetic component, we find a non-linear increase of the critical temperature with the concentration in the form of $T_{c}\propto p^{n/d}$, depending on the system dimensionality $d$ and the index $n$, whereas $n > d$.

Paul B. Slater

J. M. P. Carmelo, Peter Horsch, P.-A. Bares +1 more

The Landau-Luttinger liquid formulation is used to investigate the physics of the one-dimensional Hubbard model in a magnetic field of arbitrary strength H. The low lying charge and spin excitations are studied. A novel branch of sound wave-like spin excitations arises for H>0. The low temperature thermodynamics is considered in some detail.

Masanori Ohya, Dėnes Petz