Abstract
The criticality of the anisotropic Ising model on a three-node hierarchical lattice is investigated by an exact renormalisation group transformation. The phase diagram exhibits three physically different phases, namely a paramagnetic one and surface and bulk ferromagnetic ones. When J1 not=J/sub /2 not=J3, the system orders in the direction with the largest J before it orders in the bulk. The bulk para-ferromagnetic transition is separated into three different universality classes, i.e. one isotropic and two anisotropic. This phenomenon, which is quite different from that on anisotropic Bravais lattices and seems analogous to that of a semi-infinite Ising model, is analysed.
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