2 research outputs found
The one-dimensional XXZ model with long-range interactions
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
where the
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.Comment: 5 pages, 1 figure, presented at ICM2000, to be published in the
Proceedings (Journal of Magnetism & Magnetic Materials