  Using the 2D Jordan-Wigner transformation we reformulate the square-lattice
s=1/2 XY (XZ) model in terms of noninteracting spinless fermions and examine
the ground-state and thermodynamic properties of this spin system. We consider
the model with two types of anisotropy: the spatial anisotropy interpolating
between 2D and 1D lattices and the anisotropy of the exchange interaction
interpolating between isotropic XY and Ising interactions. We compare the
obtained (approximate) results with exact ones (1D limit, square-lattice Ising
model) and other approximate ones (linear spin-wave theory and exact
diagonalization data for finite lattices of up to N=36 sites supplemented by
finite-size scaling). We discuss the ground-state and thermodynamic properties
in dependence on the spatial and exchange interaction anisotropies. We pay
special attention to the quantum phase transition driven by the exchange
interaction anisotropy as well as to the appearance/disappearance of the
zero-temperature magnetization in the quasi-1D limit.
