Infinite coupling magnon theory of quantum Heisenberg magnetic models of spin s

An infinity magnon coupling term is introduced into the Holstein-Primakoff transformed forms of the Heisenberg ferromagnetic and antiferromagnetic models of any spin $s$ to rigorously remove the unphysical magnon states. This term makes the series expansion of the square root of the magnon operators become a finite series of magnon operator products. Under a simple Hubbard-like approximation our infinite coupling theory yields much better result than the existing spin wave theories, especially near transition temperatures.