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The coupling of the $c=-2$, $c=\frac{1}{2}$ and $c=0$ conformal fieldtheories are numerically considered in this paper. As the prototypes of thecouplings, $(c_1=-2)\oplus (c_2=0)$ and $(c_1=-2)\oplus (c_2=\frac{1}{2})$, weconsider the BTW model on the 2D square critical site-percolation and the BTWmodel on Ising-correlated percolation lattices respectively. Some geometricaltechniques are used to characterize the presumable conformal symmetry of theresultant systems. Using the Schramm-Loewrner evolution (SLE), we find that thealgebra of the central charges of the coupled models is closed, namely theformer case results to two-dimensional self-avoiding walk (SAW) fixed pointcorresponding to $c=0$ conformal field theory, whereas the latter one resultsto the two-dimensional critical Ising fixed point corresponding to the$c=\frac{1}{2}$ conformal field theory.

Coupling of $c=-2$ and $c=\frac{1}{2}$ and $c=0$ conformal field theories: The geometrical point of view