Study of Quantum Spin 1/2 X-Y Model by Means of Extended Migdal Approximation

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Abstract
The quantum spin 1/2 X-Y model in dimensions d = 1, 2 and 3 is studied by means of the extended Migdal approximation for the scale factor of the transformation b = 2. It is found, with the imposed conditions to get the recursion equations, that an unstable fixed point between a T = 0 fixed point and that of T = ∞ exists for d > 1. However, alternate imposed conditions lead to an unusual behavior that the T = 0 fixed point does not appear in any dimension and that a stable fixed point appears at a lower temperature than that of an unstable one for d > 2. The same model on the simple cubic and face-centered cubic lattices is also treated by the two-step decimation transformation.

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