THE EFFECT OF AN EXTERNAL MAGNETIC-FIELD ON THE MLRO IN THE GLOBAL GROUND-STATES OF SOME ANTIFERROMAGNETIC MODELS

In this paper, we shall study the effect of an external magnetic field on the magnetic long-range orders (MLRO) in the global ground states of the quantum XY model and the isotropic Heisenberg model on the simp le cubic lattices. We shall rigorously prove that, while an external m agnetic field (staggered in the antiferromagnetic case) which favours MLRO in a specific spin direction, say x-direction, is turned on, it c ompletely suppresses the MLRO in the perpendicular spin directions in the global ground states of these models.