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

T. Tatsumi | Zendy

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

Author(s) -

T. Tatsumi

Publication year - 1981

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.65.451

Subject(s) - physics , decimation , fixed point , recursion (computer science) , spin (aerodynamics) , dimension (graph theory) , simple (philosophy) , mathematical physics , transformation (genetics) , scale (ratio) , quantum mechanics , condensed matter physics , mathematical analysis , combinatorics , thermodynamics , mathematics , philosophy , biochemistry , chemistry , filter (signal processing) , algorithm , epistemology , computer science , gene , computer vision

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=O fixed point and that of T== exists for d>l. 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. Recently much attention has been paid to the X- Y model to clarify the nature of a phase transition in two dimensions. As for the quantum X- Y model, it is believed with little doubt that the one-dimensional model remains paramagnetic at all temperatures and that there occurs a second order phase transition in three dimensions to an ordered phase with the long range order (transverse magnetization) at a finite temperature.])

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