Progress of Theoretical Physics Vol. 59 No. 1 (1978) pp. 299-300 Renormalization-Group Approach to Spin Glass Transition in an Ising Model Takeshi Tatsumi Progress of Theoretical Physics Vol. 59 No. 2 (1978) pp. 405-413 Renormalization-Group Approach to Spin Glass Transition of a Random Bond Ising Model in Two- and Three-Dimensions Takeshi Tatsumi Progress of Theoretical Physics Vol. 59 No. 3 (1978) pp. 714-724 Renormalization-Group Transformation of Three-Dimensional Ising Models Takeshi Tatsumi
We present a real-space renormalization-group (RG) study of the
n-component classical Heisenberg model in the large-
n limit. We obtain exact expressions for correlation functions of block spins, given those of the original spins. We show how to extract the critical behavior of the model from such information. The model provides a good testing ground for evaluating the effectiveness of Monte Carlo RG techniques. We study numerically the implementation of the real-space RG transformation on finite lattices. In two dimensions, we obtain the $\ensuremath{\beta}$ function as a function of temperature. In three dimensions, we calculate the critical temperature and the thermal exponent. We discuss the effects of the use of finite lattices and of the use of different forms for the initial action on the accuracy of the results.