  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,
$<S_{_{j}}^{z}S_{l}^{z}>$, 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.
