Anti-Ferromagnetic Condensate in Yang-Mills Theory

Non-renormalizable models are traditionally ignored in high energy physics due to their lack of predictive power. In fact, one needs infinitely many counter terms and renormalization conditions to render these theories well defined. In the framework of the renormalization group [1] one usually identifies the ultraviolet fixed point, where the correlation length diverges with the renormalized theory [2]. In the vicinity of the fixed point the renormalization group equations can be linearized. The resulting scaling law allows to define relevant, marginal or irrelevant operators. These are the eigen-operators of the linearized renormalization group equation with increasing, constant or decreasing coefficients as the cut-off is lowered. It is of central importance that the class of relevant and marginal operators is equivalent to the class of renormalizable operators. This can be seen from a comparison of two renormalized trajectories, one with relevant or marginal couplings, the other one with additional contributions from irrelevant operators. The trajectories approach each other at the infrared end of the region of linearizability. The difference between the two theories reduces to an overall scale factor only as the cut-off