Critical behavior of the Gaussian model on fractal lattices in external magnetic field

For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the extern al magnetic field of site i in this model depend on the coordination number q(i) of site i, and that the relation b(qi)/b(qi) = q(i)/q(i) holds among b(q)'s, where b(q) is the Gaussian type distribution constant of site i. Us ing the decimation real-space renormalization group following the spin-resc aling method, the critical points and critical exponents of the Gaussian mo del are calculated on some Koch type curves and a family of the diamond-typ e hierarchical (or DH) lattices. At the critical points, it is found that t he nearest-neighbor interaction and the magnetic field of site i can be exp ressed in the form K-* = b(q)/q(i) and h(qi)(*) = 0, respectively. It is al so found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are ide ntical with the exact results on translation symmetric lattices, and if the fractal dimensionality d(f)=4, the Gaussian model and the mean field theor ies give the same results.