Kramers-Wannier symmetry and strong-weak-coupling duality in 2D Φ4 field models

It is found that the exact beta-function β(g) of the continuous 2D gΦ4 model posses 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 gc. 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