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We solve the O(n) model, defined in terms of self- and mutually avoiding loops coexisting with voids, on a 3-simplex fractal lattice, using an exact real space renormalization group technique. As the density of voids is decreased, the model shows a critical point, and for even lower densities of voids, there is a dense phase showing power-law correlations, with critical exponents that depend on n, but are independent of density. At n=-2 on the dilute branch, a trivalent vertex defect acts as a marginal perturbation. We define a model of biconnected clusters which allows for a finite density of such vertices. As n is varied, we get a line of critical points of this generalized model, emanating from the point of marginality in the original loop model. We also study another perturbation of adding local bending rigidity to the loop model, and find that it does not affect the universality class.
We show that the recent renormalization-group analysis of Lifshitz critical behavior presented by Leite [Phys. Rev. B {bf 67}, 104415 (2003)] suffers from a number of severe deficiencies. In particular, we show that his approach does not give an ultr
A two-loop renormalization group analysis of the critical behaviour at an isotropic Lifshitz point is presented. Using dimensional regularization and minimal subtraction of poles, we obtain the expansions of the critical exponents $ u$ and $eta$, the
An introduction to the theory of critical behavior at Lifshitz points is given, and the recent progress made in applying the field-theoretic renormalization group (RG) approach to $phi^4$ $n$-vector models representing universality classes of $m$-axi
Recent numerical studies of the susceptibility of the three-dimensional Ising model with various interaction ranges have been analyzed with a crossover model based on renormalization-group matching theory. It is shown that the model yields an accurat
The critical behaviour of the O(n)-symmetric model with two n-vector fields is studied within the field-theoretical renormalization group approach in a D=4-2 epsilon expansion. Depending on the coupling constants the beta-functions, fixed points and