Explicit Renormalization Group for D=2 random bond Ising model with long-range correlated disorder

We investigate the explicit renormalization group for fermionic field theoretic representation of two-dimensional random bond Ising model with long-range correlated disorder. We show that a new fixed point appears by introducing a long-range correlated disorder. Such as the one has been observed in previous works for the bosonic ($\phi^4$) description. We have calculated the correlation length exponent and the anomalous scaling dimension of fermionic fields at this fixed point. Our results are in agreement with the extended Harris criterion derived by Weinrib and Halperin.Comment: 5 page

Chiral phase transitions: focus driven critical behavior in systems with planar and vector ordering

The fixed point that governs the critical behavior of magnets described by the $N$-vector chiral model under the physical values of $N$ ($N =2, 3$) is shown to be a stable focus both in two and three dimensions. Robust evidence in favor of this conclusion is obtained within the five-loop and six-loop renormalization-group analysis in fixed dimension. The spiral-like approach of the chiral fixed point results in unusual crossover and near-critical regimes that may imitate varying critical exponents seen in physical and computer experiments.Comment: 4 pages, 5 figures. Discussion enlarge

The Harris-Luck criterion for random lattices

The Harris-Luck criterion judges the relevance of (potentially) spatially correlated, quenched disorder induced by, e.g., random bonds, randomly diluted sites or a quasi-periodicity of the lattice, for altering the critical behavior of a coupled matter system. We investigate the applicability of this type of criterion to the case of spin variables coupled to random lattices. Their aptitude to alter critical behavior depends on the degree of spatial correlations present, which is quantified by a wandering exponent. We consider the cases of Poissonian random graphs resulting from the Voronoi-Delaunay construction and of planar, ``fat'' $\phi^3$ Feynman diagrams and precisely determine their wandering exponents. The resulting predictions are compared to various exact and numerical results for the Potts model coupled to these quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one figure added for clarification, minor re-wordings and typo cleanu

Critical behavior of the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy

We study the two-dimensional N-component Landau-Ginzburg Hamiltonian with cubic anisotropy. We compute and analyze the fixed-dimension perturbative expansion of the renormalization-group functions to four loops. The relations of these models with N-color Ashkin-Teller models, discrete cubic models, planar model with fourth order anisotropy, and structural phase transition in adsorbed monolayers are discussed. Our results for N=2 (XY model with cubic anisotropy) are compatible with the existence of a line of fixed points joining the Ising and the O(2) fixed points. Along this line the exponent $\eta$ has the constant value 1/4, while the exponent $\nu$ runs in a continuous and monotonic way from 1 to $\infty$ (from Ising to O(2)). For N\geq 3 we find a cubic fixed point in the region $u, v \geq 0$, which is marginally stable or unstable according to the sign of the perturbation. For the physical relevant case of N=3 we find the exponents $\eta=0.17(8)$ and $\nu=1.3(3)$ at the cubic transition.Comment: 14 pages, 9 figure

Critical behavior of magnetic systems with extended impurities in general dimensions

We investigate the critical properties of d-dimensional magnetic systems with quenched extended defects, correlated in $\epsilon_d$ dimensions (which can be considered as the dimensionality of the defects) and randomly distributed in the remaining $d-\epsilon_d$ dimensions; both in the case of fixed dimension d=3 and when the space dimension continuously changes from the lower critical dimension to the upper one. The renormalization group calculations are performed in the minimal subtraction scheme. We analyze the two-loop renormalization group functions for different fixed values of the parameters $d, \epsilon_d$. To this end, we apply the Chisholm-Borel resummation technique and report the numerical values of the critical exponents for the universality class of this system.Comment: 8 figures. To appear in Phys. Rev.