摘要: The calculation of the critical exponents of the n-vector model in 3 dimensions is discussed using field theoretical techniques. This calculation is based on a perturbative expansion at fixed dimensions of the various renormalizat... 展开 The calculation of the critical exponents of the n-vector model in 3 dimensions is discussed using field theoretical techniques. This calculation is based on a perturbative expansion at fixed dimensions of the various renormalization group (R.G.) functions. Since in 3 dimensions the fixed point S exp 4 coupling constant is not small, the perturbative expansion has to be resummed. A summation technique is presented using a Borel transformation and a conformal mapping on the variable, argument of the Borel transform. Such a conformal mapping has been made possible by the existence of methods to evaluate the large order behavior of perturbation theory. In addition the application of the same summation technique to the n=1 (Ising like) S exp 4 model in two dimensions, and the Wilson-Fisher epsilon-expansion is presented also. Finally the n=1, d=3 results for the exponents are compared with results obtained by analyzing the longer B.C.C. high temperature (H.T.) series obtained by Nickel, which seem to have eliminated the discrepancies between the R.G. predictions and lattice model calculations. (Atomindex citation 12:633302) 收起