Critical behaviour of the discrete n-vector model in a planar self-dual lattice: a renormalization group approach

Within a real-space renormalization group which preserves two-site correlation functions, the authors study, for all values and signs of the coupling constants, the criticality of an extended version of the cubic model (C(n)). All results are exact for the associated planar self-dual hierarchical lattice. The phase diagram typically exhibits five different phases. The n-evolution (for n real) of the thermal and crossover critical exponents is determined as well. In addition, they present an operational procedure (the break-collapse method) which considerably simplifies the exact calculation of the correlation function associated with two-terminal C(n) graphs.

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