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The mixed spin-1/2 and spin-3/2 Ising model on the extended Kagom'e lattice is solved by establishing a mapping correspondence with the eight-vertex model. When the parameter of uniaxial single-ion anisotropy tends to infinity, the model system becomes exactly solvable as the staggered eight-vertex model satisfying the free-fermion condition. The critical points within this manifold can be characterized by critical exponents from the standard Ising universality class. The critical points within another subspace of interaction parameters, which corresponds to a coexistence surface between two ordered phases, can be approximated by corresponding results of the uniform eight-vertex model satisfying the zero-field condition. This coexistence surface is bounded by a line of bicritical points that have non-universal continuously varying critical indices

Non-universal critical behaviour of a mixed-spin Ising model on the extended Kagomé lattice