We discuss the analytic properties of the Callan-Symanzik beta -function beta (g) associated with the zero-momentum four-point coupling g in the two-dimensional phi (4) model with O(N) symmetry. Using renormalization-group arguments, we derive the asymptotic behaviour of beta (g) at the fixed point g*. We argue that beta'(g) = beta'(g*)+ O(\g - g*\(1/7)) for N = 1 and beta'(g) = beta'(g*) + O(1/log\g - g*\) for N greater than or equal to 3. Our claim is supported by an explicit calculation in the Ising lattice model and by a 1/N calculation for the two-dimensional phi (4) theory. We discuss how these non-analytic corrections may give rise to a slow convergence of the perturbative expansion in powers of g.

Non-analyticity of the Callan-Symanzik beta-function of two-dimensional O(N) models

Calabrese, Pasquale;
2000

Abstract

We discuss the analytic properties of the Callan-Symanzik beta -function beta (g) associated with the zero-momentum four-point coupling g in the two-dimensional phi (4) model with O(N) symmetry. Using renormalization-group arguments, we derive the asymptotic behaviour of beta (g) at the fixed point g*. We argue that beta'(g) = beta'(g*)+ O(\g - g*\(1/7)) for N = 1 and beta'(g) = beta'(g*) + O(1/log\g - g*\) for N greater than or equal to 3. Our claim is supported by an explicit calculation in the Ising lattice model and by a 1/N calculation for the two-dimensional phi (4) theory. We discuss how these non-analytic corrections may give rise to a slow convergence of the perturbative expansion in powers of g.
33
46
8155
8170
Calabrese, Pasquale; Caselle, M; Celi, A; Pelissetto, A; Vicari, E.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/15023
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 59
  • ???jsp.display-item.citation.isi??? 49
social impact