Das antiferromagnetische Heisenberg-Modell in der Valence-Bond-Darstellung

We study the thermodynamical behaviour of the quantum spin 1/2 Heisenberg model in one, two and three dimensions. Starting from the valence bond representation final rings up to 16 sites can be calculated exactly and evolution equations for the thermodynamical limit can be solved approximately. The exact results on finite rings are in agreement with other methods. Introducing competing interactions the phase transition from the antiferromagnetic to the frustrated phase is examined. The approximations for the thermodynamical limit are in agreement with the high temperature expansions in d = 1, 1 and 3. Furthermore the energy and the staggered magnetization in the ground state can be described very well. The approximations lead to a meanful like phase transition in d = 3. (orig.)SIGLEAvailable from TIB Hannover: RO 9740(95-3) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman