We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic interaction and compute the renormalization-group functions to six-loop order in d=3. We analyze the stability of the fixed points using a Borel transformation and a conformal mapping that takes into account the singularities of the Borel transform. We find that the cubic fixed point is stable for N>N-c, N-c=2.89(4). Therefore, the critical properties of cubic ferromagnets are not described by the Heisenberg isotropic Hamiltonian, but instead by the cubic model at the cubic fixed point. For N=3, the critical exponents at the cubic and symmetric fixed points differ very little (less than the precision of our results, which is less than or similar to 1% in the case of gamma and nu). Moreover? the irrelevant interaction bringing from the symmetric to the cubic fixed point gives rise to slowly decaying scaling corrections with exponent omega(2)=0.010(4). For N=2, the isotropic fixed point is stable and the cubic interaction induces scaling corrections with exponent omega(2)=0.103(8). These conclusions are confirmed by a similar analysis of the five-loop epsilon expansion. A constrained analysis, which takes into account that N-c=2 in two dimensions, gives N-c=2.87(5).

N-component Ginzburg-Laudau Hamiltonian with cubic anisotropy: A six-loop study / J. M., Carmona; Pelissetto, Andrea; E., Vicari. - In: PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS. - ISSN 1098-0121. - STAMPA. - 61(2000), pp. 15136-15151. [10.1103/physrevb.61.15136]

N-component Ginzburg-Laudau Hamiltonian with cubic anisotropy: A six-loop study

PELISSETTO, Andrea;
2000

Abstract

We consider the Ginzburg-Landau Hamiltonian with a cubic-symmetric quartic interaction and compute the renormalization-group functions to six-loop order in d=3. We analyze the stability of the fixed points using a Borel transformation and a conformal mapping that takes into account the singularities of the Borel transform. We find that the cubic fixed point is stable for N>N-c, N-c=2.89(4). Therefore, the critical properties of cubic ferromagnets are not described by the Heisenberg isotropic Hamiltonian, but instead by the cubic model at the cubic fixed point. For N=3, the critical exponents at the cubic and symmetric fixed points differ very little (less than the precision of our results, which is less than or similar to 1% in the case of gamma and nu). Moreover? the irrelevant interaction bringing from the symmetric to the cubic fixed point gives rise to slowly decaying scaling corrections with exponent omega(2)=0.010(4). For N=2, the isotropic fixed point is stable and the cubic interaction induces scaling corrections with exponent omega(2)=0.103(8). These conclusions are confirmed by a similar analysis of the five-loop epsilon expansion. A constrained analysis, which takes into account that N-c=2 in two dimensions, gives N-c=2.87(5).
File allegati a 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/11573/75455
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 152
  • ???jsp.display-item.citation.isi??? 139
social impact