Hierarchic trees with branching number close to one: Noiseless Kardar-Parisi-Zhang equation with additional linear term for imitating two-dimensional and three-dimensional phase transitions.
An imitation of two-dimensional (2D) field theory is formulated by means of a model on the hierarchic tree (with branching number close to one) with the same potential and the free correlators identical to 2D correlator ones. Such a model carries on some features of the original model for certain scale invariant theories. The renormalization group equation for the free energy is the noiseless Kardar-Parisi-Zhang equation with an additional linear term.
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