Critical exponents for Ising-like systems on Sierpinski carpets

B. Bonnier , Y. Leroyer , C. Meyers

The critical properties of Ising models on various fractal lattices of the Sierpinski carpet type are studied using numerical simulations. We observe scaling and measure the exponents γ and ν which are then compared to the values which have been recently extrapolated from the Wilson-Fisher ε-expansion in non integer dimensions. It appears that in the general case an effective dimension, in addition to the Hausdorf dimension, is needed to describe the critical behaviour. When these dimensions are equal, our results are then compatible with the conjecture that the fractal lattice could interpolate regular lattices in non integer dimensions.

Mots clés: critical phenomena; fractals; Ising model; lattice theory and statistics

Domaines: Articles anciens

B. Bonnier, Y. Leroyer, C. Meyers. Critical exponents for Ising-like systems on Sierpinski carpets. Journal de Physique, 1987, 48 (4), pp.553-558. ⟨10.1051/jphys:01987004804055300⟩. ⟨jpa-00210469⟩