Abstract

The strong-weak coupling symmetry in 2D Φ^4 field models

Highlights

  • The 2D Ising model and some other lattice spin models are known to possess the remarkable Kramers-Wannier(KW) duality symmetry, playing an important role both in statistical mechanics, quantum field theory [1,2] and in superstring models [3]

  • In this paper we study other duality symmetries of the beta-function β(g) for the 2D gΦ4 theory regarded as a non-integrable continuum limit of the exactly solvable 2D Ising model

  • We have shown that the β-function of the 2D gΦ4 theory does have the two types of dual symmetries, these being the Kramers-Wannier symmetry and the weakstrong coupling symmetry (S-duality)

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Summary

Introduction

The 2D Ising model and some other lattice spin models are known to possess the remarkable Kramers-Wannier(KW) duality symmetry, playing an important role both in statistical mechanics, quantum field theory [1,2] and in superstring models [3]. B.N.Shalaev symmetry was extended to the continuous 2D gΦ4 model [5] in the strong-coupling regime, i.e. for g > g∗ This beta-function β(g) is to date known only in the five-loop approximation within the framework of the conventional perturbation theory at the fixed dimension d = 2 [6]. The strong coupling expansion for the calculation of the beta-function of the 2D scalar gΦ4 theory as an alternative approach to the convemtional perturbation theory (described in the excellent textbook, known among experts in the field as Bible [7]) and was developed in [8] It is well known from quantum field theory and statistical mechanics that any strong coupling expansions are closely connected with the high-temperature (HT) series expansions for lattice models.

The correlation length and the Coupling constant
The Kramers-Wannier symmetry
The weak-strong coupling dual symmetry
Higher-order terms of the beta-function
Discussion and concluding remarks

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