Abstract:
The method proposed earlier for investigating the dynamics of the isotropic Heisenberg paramagnet at high temperatures is generalized to the anisotropic case. A system of nonlinear integrodifferential equations relating the three autocorrelation functions of the x, y, and z components of an individual spin is obtained. A solution of the system is sought in the form of a series in powers of the time and is investigated on the plane of the complex time variable. The coefficients of the series up to the tenth order for the xy model and the model with truncated dipole interaction are calculated, and the parameters of the singular points nearest the origin are determined from them.
Citation:
V. E. Zobov, “Autocorrelation functions of the anisotropic Heisenberg paramagnet in the approximation of a self-consistent fluctuating field”, TMF, 84:1 (1990), 111–119; Theoret. and Math. Phys., 84:1 (1990), 751–757
This publication is cited in the following 9 articles:
Zobov V.E., Kucherov M.M., “Exponential Bound For the Heating Rate of Periodically Driven Spin Systems”, J. Exp. Theor. Phys., 128:4 (2019), 641–649
V. E. Zobov, M. M. Kucherov, “On the effect of an inhomogeneous magnetic field on high-frequency asymptotic behaviors of correlation functions of spin lattices”, JETP Letters, 107:9 (2018), 553–557
A. G. Lundin, V. E. Zorin, “Nuclear magnetic resonance in condensed matter”, Phys. Usp., 50:10 (2007), 1053–1077
V. E. Zobov, M. A. Popov, “The Coordinate of the Singular Point of Generating Functions of Clusters in the High-Temperature Dynamics of Spin Lattice Systems with Axially Symmetric Interaction”, Theoret. and Math. Phys., 136:3 (2003), 1297–1311
V. E. Zobov, M. A. Popov, “On the Coordinate of a Singular Point of the Time Correlation Function for a Spin System on a Simple Hypercubic Lattice at High Temperatures”, Theoret. and Math. Phys., 131:3 (2002), 862–872
V. E. Zobov, A. A. Lundin, O. E. Rodionova, “The shape of NMR absorption and cross-relaxation spectra in a heteronuclear spin system”, J. Exp. Theor. Phys., 93:3 (2001), 542
V. E. Zobov, “Singular points of time-dependent correlation functions of spin systems on large-dimensional lattices at high temperatures”, Theoret. and Math. Phys., 123:1 (2000), 511–523
V. L. Bodneva, A. A. Lundin, A. A. Milyutin, “On possibility of using the reduced description of the anisotropic Heisenberg paramagnet spin dynamics, and the NMR line-shape in solids”, Theoret. and Math. Phys., 106:3 (1996), 370–384
V. E. Zobov, M. A. Popov, “Dynamics of a system with three-spin interection in the Gaussian fluctuating local field approximation”, Theoret. and Math. Phys., 102:2 (1995), 224–234
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