  Phase diagram, critical properties and thermodynamic functions of the
two-dimensional field-free quantum-spin-1/2 XXZ model has been calculated
globally using a numerical renormalization group theory. The nearest-neighbor
spin-spin correlations and entanglement properties, as well as internal energy
and specific heat are calculated globally at all temperatures for the whole
range of exchange interaction anisotropy, from XY limit to Ising limits, for
both antiferromagnetic and ferromagnetic cases. We show that there exists
long-range (quasi-long-range) order at low-temperatures, and the low-lying
excitations are gapped (gapless) in the Ising-like easy-axis (XY-like
easy-plane) regime. Besides, we identify quantum phase transitions at
zero-temperature.
