Fixed point stability and decay of correlations

Ettore Vicari (1) , Jean Zinn-Justin (2)

1 Dipartimento di Fisica, Ist Nazl Fis Nucl
2 DAPNIA - Département d'Astrophysique, de physique des Particules, de physique Nucléaire et de l'Instrumentation Associée

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.

Keywords: ORDER PARAMETERS; RENORMALIZATION-GROUP ANALYSIS; EQUATION-OF-STATE; N-VECTOR MODEL; CRITICAL EXPONENTS; PHASE-TRANSITIONS; TETRACRITICAL POINTS; 4 DIMENSIONS; FIELD-THEORY; PHYSICAL REALIZATIONS

Domains: General Physics [physics.gen-ph]

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