Journal of Physical Studies 5(3/4), 240–245 (2001)
DOI: https://doi.org/10.30970/jps.05.240 KRAMERS–WANNIER SYMMETRY AND STRONG-WEAK-COUPLING DUALITY IN 2D Φ4 FIELD MODELSB. N. Shalaev
A. F. Ioffe Physical \& Technical Institute,
Russian Academy of Sciences, |
It is found that the exact beta-function $β(g)$ of the continuous 2D $gΦ^{4}$ model possesses two types of dual symmetries, these being the Kramers-Wannier (KW) duality symmetry and the weak-strong-coupling symmetry $f(g)$ (or $S$-duality). All these transformations are explicitly constructed. The $S$-duality transformation $f(g)$ is shown to connect domains of weak and strong couplings, i.e., above and below $g_{c}$. Basically, it means that there is a tempting possibility to compute multiloop Feynman diagrams for the $β$-function using high-temperature lattice expansions. The regular scheme developed is found to be strongly unstable. Approximate values of the renormalized coupling constant $g^{*}_{+}$ found from duality symmetry equations are in a good agreement with the available numerical results.
PACS number(s): 74.20.-z, 05.10.Cc, 11.25.Hf