  The one-dimensional extended isotropic XY model (s=1/2) in a transverse field
with uniform long-range interactions among the \textit{z} components of the
spin is considered. The model is exactly solved by introducing the gaussian and
Jordan-Wigner transformations, which map it in a non-interacting fermion
system. The partition function can be determined in closed form at arbitrary
temperature and for arbitrary multiplicity of the multiple spin interaction.
  From this result all relevant thermodynamic functions are obtained and, due
to the long-range interactions, the model can present classical and quantum
transitions of first- and second-order. The study of its critical behavior is
restricted for the quantum transitions, which are induced by the transverse
field at $T=0.$ The phase diagram is explicitly obtained for multiplicities
$p=2,3,4$ and $\infty ,$ as a function of the interaction parameters, and, in
these cases, the critical behavior of the model is studied\textbf{\}in detail.
Explicit results are also presented for the induced magnetization and
isothermal susceptibility $\chi_{T}^{zz}$, and a detailed analysis is also
carried out for the static longitudinal $<S_{j}^{z}S_{l}^{z}>$ and transversal
$<S_{j}^{x}S_{l}^{x}>$ correlation functions. The different phases presented by
the model can be characterized by the spatial decay of the these correlations,
and from these results some of these can be classified as quantum spin liquid
phases. The static critical exponents and the dynamic one, $z,$ have also been
determined, and it is shown that, besides inducing first order phase
transition, the long-range interaction also changes the universality class the
model.-range interaction also changes the universality class the model.
