Exact boson representation of quantum spin systems and investigation of their critical behavior

Quantum spin systems are shown to be rigorously equivalent to certain Bose systems. As a result the phase transitions occuring in such systems can be regarded as generalized Bose condensation processes. In those processes it is not the number of bosons that is kept constant but a certain function of it. The problem of degeneracy arising in Bosonizing a spin system is solved in a simple fashion. The low-temperature limit of the Bose systems reproduces the magnon gas with correct interactions. The Bloch sum rule becomes exact at all temperatures, when one replaces the magnon number by the number of bosons. The crossover to classical behavior at criticality is discussed and it is shown that at $T_c$ the quantum $S=\frac{1}{2}$ spin systems behave like the corresponding classical $S=\infty$ systems. A classical effective Hamiltonian whose corresponding partition function is equal to the partition function of the quantum spin systems is derived. Finally, possible application to dynamics are briefly discussed.