  The nonlinear sigma-model and its generalization on N-component spins, the
O(N) model, are considered to describe thermodynamics of a quantum
quasi-two-dimensional (quasi-2D) Heisenberg antiferromagnet. A comparison with
standard spin-wave approaches is performed. The sublattice magnetization, Neel
temperature and spin correlation function are calculated to first order of the
1/N-expansion. A description of crossover from a 2D-like to 3D regime of
sublattice magnetization temperature dependence is obtained. The values of the
critical exponents derived are \beta =0.36, \eta =0.09. An account of the
corrections to the standard logarithmic term of the spin-wave theory modifies
considerably the value of the Neel temperature. The thermodynamic quantities
calculated are universal functions of the renormalized interlayer coupling
parameter. The renormalization of interlayer coupling parameter turns out to be
considerably temperature dependent. A good agreement with experimental data on
La2CuO4 is obtained. The application of the approach used to the case of a
ferromagnet is discussed.
