Real-space renormalization-group study of fractal Ising models

Abstract

Ising models on Sierpi\ifmmode \acute{n}\else \'{n}\fi{}ski carpets are studied within a real-space renormalization technique. A specific method for decimating spin blocks of any size is proposed as an alternative to the bond-moving prescription, and its accuracy is checked on various examples. From an analysis of the critical couplings we estimate some of the finite-size effects of Monte Carlo simulations of fractals. The exponent \ensuremath{\nu}, computed for a large variety of carpets, is found smaller than in the bond-moving approach but with the same behavior under variations of the fractal parameters. No universality criterion emerges except in the limit of vanishing lacunarity.