5. Phyls. A: Math. Gen. 28 (L995) L73-L78. Printed in the UK LETTER TO THE EDITOR

Abstract. We use a histogram Monte Carlo simulation method to calculate the scaling funetions of the existence probability EB and the percolation probability P of the bond random pncolation model on honeycomb lattices with aspect ratios of 0 5 and 20. We find &at such different aspect ratios give quite different scaling functions near the critic $ region. However, they give a consistent a'itical point, critical exponents. and the thermodynamic order parameter from renormalization-group calculations. Some interesting theoretical problems related to this work are discussed. Finite-size scaling has been an important subject of reseqch in recent~decades 11-61. According to the theory of finite-size scaling [ I 4 1 if the dependence of a physical quantity Q of a thennodynamic system on the parameter t, which vanishes at the critical point, may be written as Q(t) - tu near the critical point, then for a finite system of linear dimension L at t, the corresponding quantity Q(L, t) may be written as.. Q(L, f)- L-?"F(tLn) ( 1) where yt ( = u-l) is the thermal scaling power and F ( x) , x = tLn, is called a scaling function. When finitesize scaling is valid, the scaled dap Q ( L, t)/L-"n for differen