Critical behavior of generic competing systems

Details Critical behavior of generic competing systems Critical behavior of generic competing systems

2005-02-04

arxiv.org/abs/cond-mat/0502136v2

Physics

Condensed Matter

Statistical Mechanics

RevTex, 54 pages, 3 figures; version accepted for publication in Physical Review B

Scientific paper

10.1103/PhysRevB.72.224432

Generic higher character Lifshitz critical behaviors are described using field theory and $\epsilon_{L}$-expansion renormalization group methods. These critical behaviors describe systems with arbitrary competing interactions. We derive the scaling relations and the critical exponents at the two-loop level for anisotropic and isotropic points of arbitrary higher character. The framework is illustrated for the $N$-vector $\phi^{4}$ model describing a $d$-dimensional system. The anisotropic behaviors are derived in terms of many independent renormalization group transformations, each one characterized by independent correlation lengths. The isotropic behaviors can be understood using only one renormalization group transformation. Feynman diagrams are solved for the anisotropic behaviors using a new dimensional regularization associated to a generalized orthogonal approximation. The isotropic diagrams are treated using this approximation as well as with a new exact technique to compute the integrals. The entire procedure leads to the analytical solution of generic loop order integrals with arbitrary external momenta. The property of universality class reduction is also satisfied when the competing interactions are turned off. We show how the results presented here reduce to the usual $m$-fold Lifshitz critical behaviors for both isotropic and anisotropic criticalities.

Affiliated with

Also associated with

No associations

Rating

Critical behavior of generic competing systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Critical behavior of generic competing systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critical behavior of generic competing systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-527928