  Modifying the conventional spin-wave theory in a novel manner based on the
Wick decomposition, we present an elaborate thermodynamics of square-lattice
quantum antiferromagnets. Our scheme is no longer accompanied by the notorious
problem of an artificial transition to the paramagnetic state inherent in
modified spin waves in the Hartree-Fock approximation. In the cases of spin
$\frac{1}{2}$ and spin $1$, various modified-spin-wave findings for the
internal energy, specific heat, static uniform susceptibility, and dynamic
structure factor are not only numerically compared with quantum Monte Carlo
calculations and Lanczos exact diagonalizations but also analytically expanded
into low-temperature series. Modified spin waves interacting via the Wick
decomposition provide reliable thermodynamics over the whole temperature range
of absolute zero to infinity. Adding higher-order spin couplings such as ring
exchange interaction to the naivest Heisenberg Hamiltonian, we precisely
reproduce inelastic-neutron-scattering measurements of the
high-temperature-superconductor-parent antiferromagnet
$\mathrm{La}_2\mathrm{CuO}_4$. Modifying Dyson-Maleev bosons combined with
auxiliary pseudofermions also yields thermodynamics of square-lattice
antiferromagnets free from thermal breakdown, but it is less precise unless
temperature is sufficiently low. Applying all the schemes to layered
antiferromagnets as well, we discuss the advantages and disadvantages of
modified spin-wave and combined boson-pseudofermion representations.
