Fixed point stability and decay of correlations

Details Fixed point stability and decay of correlations Fixed point stability and decay of correlations

2006-11-14

arxiv.org/abs/cond-mat/0611353v1

New J.Phys. 8 (2006) 321

Physics

Condensed Matter

Statistical Mechanics

16 pages

Scientific paper

10.1088/1367-2630/8/12/321

In the framework of the renormalization-group theory of critical phenomena, a quantitative description of many continuous phase transitions can be obtained by considering an effective $\Phi^4$ theories, having an N-component fundamental field $\Phi_i$ and containing up to fourth-order powers of the field components. Their renormalization-group flow is usually characterized by several fixed points. We give here strong arguments in favour of the following conjecture: the stable fixed point corresponds to the fastest decay of correlations, that is, is the one with the largest values of the critical exponent $\eta$ describing the power-law decay of the two-point function at criticality. We prove this conjecture in the framework of the $\epsilon$-expansion. Then, we discuss its validity beyond the $\epsilon$-expansion. We present several lower-dimensional cases, mostly three-dimensional, which support the conjecture. We have been unable to find a counterexample.

Affiliated with

Also associated with

No associations

Rating

Fixed point stability and decay of correlations 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 Fixed point stability and decay of correlations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fixed point stability and decay of correlations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-487612