Wegner-Houghton equation in low dimensions
J.M. Carmona, J. Polonyi, A. Tarancon
TL;DR
This paper investigates scalar field theories in low dimensions using the Wegner-Houghton renormalization group, revealing non-perturbative infrared behavior and developing a lattice version of the WHRG in two dimensions.
Contribution
It introduces a lattice formulation of the Wegner-Houghton RG in two dimensions and analyzes non-perturbative infrared regimes in low-dimensional scalar theories.
Findings
Models are non-perturbative in the infrared in two dimensions and below.
Results are regularization-independent.
Develops a lattice version of the WHRG in two dimensions.
Abstract
We consider scalar field theories in dimensions lower than four in the context of the Wegner-Houghton renormalization group equations (WHRG). The renormalized trajectory makes a non-perturbative interpolation between the ultraviolet and the infrared scaling regimes. Strong indication is found that in two dimensions and below the models with polynomial interaction are always non-perturbative in the infrared scaling regime. Finally we check that these results do not depend on the regularization and we develop a lattice version of the WHRG in two dimensions.
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