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 $T_c<~T<~\infty$. In particular, we find a possibly exact result for the connectedness-length exponent ${\nu }_p=\frac{\ln \sqrt{3}}{\ln \left(\frac{3}{2}\right)}$ in the "pure" percolation ($T=\infty$) limit, which holds for $T_c<T<~\infty$. At $T=T_c$ we find the connectedness-length exponents of the percolation problem to be identical to the correlation-length exponents for the thermal problem.