Renormalization group solution of the one-dimensional classical Heisenberg model

It is shown that the method of Van Leeuwen1,2) and Nauenberg and Nienhuis3) in the application of the renormalization theory to Ising-like spin systems, can easily be extended to include all one-dimensional classical spin systems with nearest neighbor interactions. The series for the free energy converges very rapidly towards the known exact value (for Heisenberg interaction), provided that the temperature is not too close to the critical temperature T = 0.