Singular points of time-dependent correlation functions of spin systems onlarge-dimensional lattices at high temperatures

Time-dependent autocorrelation functions are investigated for the Heisenber g model with spins 1/2 on d-dimensional simple cubic lattices of large dime nsions d at infinite temperature. The autocorrelation function on the imagi nary time axis is interpreted as the generating function of bond trees cons tructed with double bonds. These trees provide the leading terms with respe ct to lid for the time-expansion coefficients of the autocorrelation functi on. The correction terms from branch intersections to the generating functi on in the Bethe approximation are derived for these trees. A procedure is s uggested for finding the correction to the coordinate of the singular point of the generating function (i.e., to the reciprocal of the branch growth-r ate parameter) from the above correction terms without calculating the numb er of trees. The leading correction terms of order 1/sigma(2) (where sigma = 2d - 1) are found for the coordinates of the singular points of the autoc orrelation function in question and for the generating function of the tree s constructed with single bonds in the Eden model.