Temperature behavior of the magnon modes of the square-lattice antiferromagnet

A spin-wave theory of short-range order in the square-lattice Heisenberg antiferromagnet is formulated. With growing temperature from T=0 a gapless mode is shown to arise simultaneously with opening a gap in the conventional spin-wave mode. The spectral intensity is redistributed from the latter mode to the former. For low temperatures the theory reproduces results of the modified spin-wave theory by Takahashi [Phys. Rev. B 40, 2494 (1989)] and Hirsch rt al. [Phys. Rev. B 40, 5000 (1989)], and without fitting parameters gives values of observables in good agreement with Monte Carlo results in the temperature range 0 less than or equal to T less than or similar to 0.8J where J is the exchange constant.