Thermodynamic functions for a model antiferromagnet with identical coupling between all spins

摘要

A model antiferromagnet consisting of N spins S=1/2, all interacting among themselves with equal strength, and with the external magnetic field H, was analysed, both for Ising spins and vector spins. Starting from the Hamiltonian, the partition function, specific heat and magnetic susceptibility vs temperature T have been calculated for both systems, for finite N (with the interspin coupling I &amp;lt; 0) and for N (yields)(infinity) (with the coupling I/N &amp;lt; 0). For finite N one finds several relations between the features of the energy levels and the calculated plots, related especially to the number of spins being odd or even. The 1/(NT) behavior of the susceptibility at T(yields) 0 for odd N has been interpreted as due to the occurrence of a single frustrated spin pushing the whole system to behave like the free spin in the external magnetic field. For N(yields)(infinity) (thermodynamic limit) the Kac procedure has been extended to include the effect of magnetic field, both for Ising spins and the vector spins. As compared with the ferromagnetic case, the evaluation of the partition function and related functions is in the case of antiferromagnetic coupling (I < 0) relatively straightforward. We have found the specific heat (per one spin) vs T at finite magnetic field to be proportional to the squared field, turning to zero at the absence of the field. The magnetic susceptibility (per one spin) shows a regular behavior of the paramagnetic type at all temperatures. (author) 8 refs, 8 figs