Accurate critical exponents for Ising like systems in non-integer dimensions

2014 In a recent article we have shown that, by applying sophisticated summation methods to Wilson-Fisher’s 03B5-expansion, it is possible from the presently known terms of the series to obtain accurate values of critical exponents for the 0 ( n ) symmetric n-vector model : these values are consistent with the best estimates obtained from threedimensional Renormalization Group calculations and, in the case of Ising-like systems, with the exactly known twodimensional values of the Ising model. The controversial conjecture has been recently formulated that some fractal lattices could interpolate regular lattices in non-integer dimensions. Numerical calculations have been done for the Ising model. To allow for direct comparison with Renormalization Group values, we present here estimates for exponents in non-integer dimensions d(1 d ~4). By imposing the exactly known 2 d values, we at the same time improve the previous 3 d estimates. Finally we find indications that for 1 d 2 the Renormalization Group values are consistent with those obtained from the near planar interface model. J. Physique 48 (1987) 19-24 JANVIER 1987, Classification Physics Abstracts ,