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

J.C. Le Guillou , J. Zinn-Justin

In a recent article we have shown that, by applying sophisticated summation methods to Wilson-Fisher's ε-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 three-dimensional Renormalization Group calculations and, in the case of Ising-like systems, with the exactly known two-dimensional 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

Mots clés: critical phenomena; fractals; Ising model; renormalisation

Domaines: Articles anciens

J.C. Le Guillou, J. Zinn-Justin. Accurate critical exponents for Ising like systems in non-integer dimensions. Journal de Physique, 1987, 48 (1), pp.19-24. ⟨10.1051/jphys:0198700480101900⟩. ⟨jpa-00210418⟩