Fixed point stability and decay of correlations

Abstract

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.

16 pages

References in corpus (3)

• The critical exponents of the superfluid transition in He4
• The critical equation of state of the three-dimensional O(N) universality class: N>4
• Spin-density-wave order in cuprates

Cited by in corpus (2)

• Multicritical behavior of two-dimensional anisotropic antiferromagnets in a magnetic field
• Disordered O(n) Loop Model and Coupled Conformal Field Theories