ON THE RADIUS OF CONVERGENCE OF SERIES IN POWERS OF TIME FOR SPIN CORRELATION-FUNCTIONS OF THE HEISENBERG MAGNET AT HIGH-TEMPERATURE

The convergence of series in powers of time for spin autocorrelation f unctions of the Heisenberg magnet are investigated at infinite tempera tures on lattices of different dimensions d. The calculation data avai lable at the present time for the coefficients of these series are use d to estimate the corresponding radii of convergence, whose growth wit h decreasing d is revealed and explained in a self-consistent approxim ation. To this end, a simplified nonlinear equation corresponding to t his approximation is suggested and solved for the autocorrelation func tion of a system with an arbitrary number Z of nearest neighbors. The coefficients of the expansion in powers of time for the solution are r epresented in the form of trees on the Bethe lattice with the coordina tion number Z. A computer simulation method is applied to calculate th e expansion coefficients for trees embedded in square, triangular, and simple cubic lattices under the condition that the intersection of tr ee branches is forbidden. It is found that the excluded volume effect that manifests itself in a decrease in these coefficients and in an in crease in the coordinate and exponent of the singularity of the autoco rrelation function on the imaginary time axis is intensified with decr easing lattice dimensions.