Thermodynamics of spin-½ fermions with σ-interactions

Leigh Sneddon, Robin B. Stinchcombe

The rectangular spin-s Ising ferromagnet with nearest-neighbour interactions is considered. The interaction energies are of the form s -2 J sigma i sigma j and s -2 J' sigma k sigma l , respectively for bonds in the two lattice directions, where the spin variables sigma i can take the values -s, -s+1,...,s-1,s. A transfer matrix formalism is used. By relating the largest eigenvalues of the transfer matrix for spin-s to those for spin- 1 / 2 , the leading order form for J'<<J of the spin-s critical curve is investigated. Subject to plausible assumption concerning the thermodynamic limit, the critical curve is shown to be given by K'=2s exp(-2K)(1+ epsilon ) where K=J/kT, K'=J'/kT and epsilon to 0 as K to infinity .

節夫 三沢

Ladislav Šamaj, Zoltán Bajnok

Aurel Bulgac

Gyu-Boong Jo

S. Foulon, F. Brosens, J. T. Devreese +1 more

We investigate the combined influence of a magnetic field and a harmonic interparticle interaction on the thermodynamic properties of a finite number of spin-polarized fermions in a confinement potential. This study is an extension using our path integral approach of symmetrized density matrices for identical particles. The thermodynamical properties are calculated for a three-dimensional model of N harmonically interacting spin-polarized fermions in a parabolic potential well in the presence of a magnetic field. The free energy and the internal energy are obtained for a limited number of particles. Deviations from the thermodynamical limit become negligible for about 100 or more particles, but even for a smaller number of fermions present in the well, scaling relations similar to those of the continuum approximation to the density of states are already satisfied.