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Physica A Statistical Mechanics and its Applications

The dynamical longitudinal correlation function of the Heisenberg model at low temperatures

Guy Dewel

Published Jan 1, 1976• 5 citations
Publisher
DOI
10.1016/0378-4371(76)90014-5

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The authors derive the thermodynamics and the static correlation functions for the classical Heisenberg chain with the anisotropies within a low-temperature steepest-descent approach. As regards the thermodynamics, they find agreement with transfer matrix and 'ideal-gas' phenomenological results. For the longitudinal correlation function the authors find an antiferromagnetic-type behaviour with a correlation length inversely proportional to the domain wall density. The transverse in-plane correlation function exhibits a damped oscillatory behaviour due to domain-wall-spin interference. The transverse out-of-plane correlations, on the other hand, are exponentially damped with the correlation length increasing as the easy-axis limit is approached.
The transverse and longitudinal spin-pair correlations are obtained as a function of temperature by the second-order Green's function method. The longitudinal N. N. spin-pair correlation at the ground state becomes negative for anisotropy parameter η between the X Y model (η=0) and quite near the Heisenberg model (η∼1.0). It is predicted from these results that the first-order phase transition occurs near the Heisenberg limit. For η=0.9, it occurs at a temperature τ c restricted by 2.4<τ<6.3.