Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2000-08-16
Physics
Condensed Matter
Statistical Mechanics
5 pages, 1 figure, presented at ICM2000, to be published in the Proceedings (Journal of Magnetism & Magnetic Materials)
Scientific paper
10.1016/S0304-8853(00)00690-9
The one-dimensional XXZ model (s=1/2, N sites) with uniform long-range interactions among the transverse components of the spins is considered. The Hamiltonian of the model is explicitly given by $H=J\sum_{j=1}^{N}(s_{j}^{x}s_{j+1}^{x}+s_{j}^{y}s_{j+1}^{y}) -(I/N)\sum_{j,k=1}^{N}s_{j}^{z}s_{k}^{z}-h\sum_{j=1}^{N}s_{j}^{z},$ where the $s^{x,y,z}$ are half the Pauli spin matrices. The model is exactly solved by applying the Jordan-Wigner fermionization, followed by a Gaussian transformation. In the absence of the long-range interactions (I=0), the model, which reduces to the isotropic XY model, is known to exhibit a second-order quantum phase transition driven by the field at zero temperature. It is shown that in the presence of the long-range interactions (I different from 0) the nature of the transition is strongly affected. For I>0, which favours the ordering of the transverse components of the spins, the transition is changed from second- to first-order, due to the competition between transverse and xy couplings. On the other hand, for I<0, which induces complete frustration of the spins, a second-order transition is still present, although the system is driven out of its usual universality class, and its critical exponents assume typical mean-field values.
Coutinho L. P. S.
Goncalves L. L.
Vieira André P.
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