A high temperature series renormalization group method

A new high temperature series renormalization group method is proposed. Our method differs from that of Niemeijer and van Leeuwen in the relative treatment of intracell and intercell interactions. The method is tested on the spin 12 Ising model on the triangular lattice with 3 spin cells and on the square lattice with 4 and 5 spin cells. Estimates of critical temperature, thermal and magnetic eigenvalues are given to third order for the first two cases and to fourth order for the 5 spin cells. The highest order estimates of the thermal eigenvalue are accurate to better than 1% but the estimates of the magnetic eigenvalue are less accurate.