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 MODELS B. N. Shalaev A. F. Ioffe Physical \& Technical Institute, Russian Academy of Sciences, 26 Polytechnicheskaya Str., St. Petersburg, 194021, Russia and Istituto Nazionale di Fisica Nucleare, Universita di Pavia Via Bassi, Pavia, 6–27100, Italy

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

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