Spectral renormalization group for the Gaussian model and ?^{4} theory on nonspatial networks.

Physical review. E, Statistical, nonlinear, and soft matter physics

PubMedID: 26382343

Tuncer A, Erzan A. Spectral renormalization group for the Gaussian model and ?^{4} theory on nonspatial networks. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;92(2-1):022106.
We implement the spectral renormalization group on different deterministic nonspatial networks without translational invariance. We calculate the thermodynamic critical exponents for the Gaussian model on the Cayley tree and the diamond lattice and find that they are functions of the spectral dimension, d[over ~]. THE RESULTS
are shown to be consistent with those from exact summation and finite-size scaling approaches.At d[over ~]=2, the lower critical dimension for the Ising universality class, the Gaussian fixed point is stable with respect to a ?^{4} perturbation up to second order. However, on generalized diamond lattices, non-Gaussian fixed points arise for 2