Skip to Main content Skip to Navigation
Journal articles

Fixed point stability and decay of correlations

Abstract : In the framework of the renormalization-group (RG) 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 RG flow is usually characterized by several fixed points (FPs). We give here strong arguments in favour of the following conjecture: the stable FP 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [44 references]  Display  Hide  Download
Contributor : Marianne Leriche Connect in order to contact the contributor
Submitted on : Thursday, July 12, 2007 - 12:22:41 PM
Last modification on : Tuesday, September 27, 2022 - 9:34:17 AM
Long-term archiving on: : Thursday, April 8, 2010 - 11:04:30 PM


Publisher files allowed on an open archive




Ettore Vicari, Jean Zinn-Justin. Fixed point stability and decay of correlations. New Journal of Physics, Institute of Physics: Open Access Journals, 2006, 8, pp.321. ⟨10.1088/1367-2630/8/12/321⟩. ⟨cea-00162076⟩



Record views


Files downloads