Abstract
The one-dimensional XXZ model (s=1/2) in a transverse field, with
uniform long-range interactions among the transverse components of the
spins, is studied. The model is exactly solved by introducing the
Jordan-Wigner transformation and the integral Gaussian transformation.
The complete critical behaviour and the critical surface for the quantum
and classical transitions, in the space generated by the transverse
field and the interaction parameters, are presented. The crossover lines
for the various classical/quantum regimes are also determined exactly.
It is shown that, besides the tricritical point associated with the
classical transition, there are also two quantum critical points: a
bicritical point where the classical second-order critical line meets
the quantum critical line, and a first-order transition point at zero
field. It is also shown that the phase diagram for the first-order
classical/quantum transitions presents the same structure as for the
second-order classical/quantum transitions. The critical classical and
quantum exponents are determined, and the internal energy, the specific
heat and the isothermal susceptibility, chi(T)(zz), are presented for
the different critical regimes. The two-spin static and dynamic
correlation functions, ((SjSlz)-S-z), are also presented, and the
dynamic susceptibility, chi(q)(zz) (omega), is obtained in closed form. Explicit results are presented at T=0, and it is shown that the
isothermal susceptibility, chi(T)(zz), is different from the static one, chi(q)(zz)(0). Finally, it is shown that, at T=0, the internal energy
close to the first-order quantum transition satisfies the scaling form
recently proposed by Continentino and Ferreira. (C) 2004 Elsevier B.V.
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