Anisotropic bond percolation in two dimensions

A new single-parameter renormalization-group equation is formulated for anisotropic bond percolation in two dimensions using a position-space renormalization approach. The new equation yields the exact critical line px+py=1 within both the Migdal-Kadanoff decimation and cell renormalization schemes. For large anisotropy, however, an additional critical line appears leading to a spurious divergence in the correlation-length critical exponent. An alternative scheme, which does not preserve the exact critical surface, but yields a correlation-length exponent relatively independent of anisotropy, is also examined.