Gap exponents for percolation processes with triangle condition

A study is made of the gap exponents for percolation processes with the triangle condition in the subcritical region. It is show that the gaps are given by_t=2 fort=2, 3,. Scaling theory predicts thatP_p(¦C₀¦S(p))–(p_c–p) andE_p(1/¦C₀¦; ¦C₀¦S(p))–(p_c–p)³, whereS(p) is the typical cluster size. It is found that (p_c–p)P_p(|C₀S(p)^1–)(p_c–p)^1–2 and (p_c–p)³E_p(1/|C₀|;|C₀|S(p)^1–))(p_c–p)^3–4.