Renormalization-Group Approach to the Percolation Properties of the Triangular Ising Model

We present a renormalization-group approach for treating the percolation properties of the nearest-neighbor triangular Ising model. We obtain exponents for the line of percolation transitions Tc<~T<~∞. In particular, we find a possibly exact result for the connectedness-length exponent νₚ=ln√3ln(3/2) in the "pure" percolation (T=∞) limit, which holds for Tc<T<~∞. At T=Tc we find the connectedness-length exponents of the percolation problem to be identical to the correlation-length exponents for the thermal problem.