The antiferromagnetic Heisenberg cube

Jozef Strečka, Jana Čisárová

A full energy spectrum of the spin-1/2 Heisenberg cubic cluster is used to investigate a low-temperature magnetization process and adiabatic demagnetization of this zero-dimensional 2 × 2 × 2 quantum spin system.It is shown that the antiferromagnetic spin-1/2 Heisenberg cube exhibits at low enough temperatures a stepwise magnetization curve with four intermediate plateaux at zero, one quarter, one half, and three quarters of the saturation magnetization.We have also found the enhanced magnetocaloric eect close to level-crossing elds that determine transitions between the intermediate plateaux.

Alessandro Pelizzola

The three-state antiferromagnetic Potts model on the simple-cubic lattice is investigated using the cluster variation method in the cube and the star-cube approximations. The broken-sublattice-symmetry phase is found to be stable in the whole low-temperature region, contrary to previous results obtained using a modified cluster variation method. The tiny free-energy difference between the broken-sublattice-symmetry and the permutationally-symmetric sublattice phases is calculated in the two approximations and turns out to be smaller in the (more accurate) star-cube approximation than in the cube one.

V. E. Korepin, N. M. Bogoliubov, Anatoli G. Izergin

Katarína Karľová, Jozef Strečka, Johannes Richter

The magnetization process and adiabatic demagnetization of antiferromagnetic spin-1/2 XXZ Heisenberg clusters in the shape of regular polyhedra (tetrahedron, octahedron, cube, icosahedron and dodecahedron) are examined using the exact diagonalization method. It is demonstrated that a quantum (xy) part of the XXZ exchange interaction is a primary cause for the presence of additional intermediate magnetization plateaux and steps, which are totally absent in the limiting Ising case. The only exception to this rule is the spin-1/2 XXZ Heisenberg tetrahedron, which shows just a quantitative shift of the level-crossing fields related to two magnetization steps. It is shown that spin-1/2 XXZ Heisenberg regular polyhedra exhibit an enhanced magnetocaloric effect in the proximity of magnetization steps and jumps, which are accompanied with a rapid drop (rise) of temperature just above (below) the level-crossing field when the magnetic field is removed adiabatically.

Carlo Heissenberg, Augusto Sagnotti