Renormalization group domains of the scalar Hamiltonian

• Date: 2000
• Main Authors: Bagnuls, C., Bervillier, C.
• Format: Article
• Language: English
• Published: Інститут фізики конденсованих систем НАН України 2000
• Series: Condensed Matter Physics
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/120996
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Renormalization group domains of the scalar Hamiltonian / C. Bagnuls, C. Bervillier // Condensed Matter Physics. — 2000. — Т. 3, № 3(23). — С. 559-575. — Бібліогр.: 28 назв. — англ.

Using the local potential approximation of the exact renormalization group (RG) equation, we show various domains of values of the parameters of the O(1) -symmetric scalar Hamiltonian. In three dimensions, in addition to the usual critical surface Sc (attraction domain of the Wilson-Fisher fixed point), we explicitly show the existence of a first-order phase transition domain Sf separated from Sc by the tricritical surface St (attraction domain of the Gaussian fixed point). Sf and Sc are two distinct domains of repulsion for the Gaussian fixed point, but Sf is not the basin of attraction of a fixed point. Sf is characterized by an endless renormalized trajectory lying entirely in the domain of negative values of the ϕ⁴ -coupling. This renormalized trajectory also exists in four dimensions making the Gaussian fixed point ultra-violet stable (and the ϕ⁴₄ renormalized field theory asymptotically free but with a wrong sign of the perfect action). We also show that a very retarded classical-to-Ising crossover may exist in three dimensions (in fact below four dimensions). This could be an explanation of the unexpected classical critical behaviour observed in some ionic systems.