Scaling and fractal dimension of Ising clusters at thed=2critical point

Abstract

Using formal arguments based on conformal invariance and on the connection between correlated-site percolation and the q-state Potts model with vacancies, we show that the exponents describing Ising clusters at Onsager’s critical point are those of the tricritical q=1 Potts model. This implies, in particular, a fractal dimension d¯=(187/96 and a percolative susceptibility exponent γ=(91/48, in good agreement with existing numerical estimates. This d¯ is also clearly supported by a new very accurate Monte Carlo finite-size scaling determination. We also conjecture an exponent ${\mathrm{y}}_{\mathrm{J}}$=(13/24 controlling the crossover between clusters and droplets.