Universality in the percolation problem—Anomalous dimensions of φ4 operators

Files
TR Number
Date
1977-05
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Abstract

We consider critical systems, such as the percolation problem, whose symmetry permits an invariant interaction of third order in the fluctuating fields φ. In the renormalization-group approach one is naturally led to look for infrared-stable fixed points which yield ε expansions in 6−ε dimensions, with ε=3 as the physical value. Since the Gaussian fixed point becomes unstable to φ4 interactions for ε>2, it is important to check that the fixed point obtained in the ε expansion remains stable to such perturbations. We report the calculation to first order in ε of the corrections to scaling induced by (stability with respect to) φ4 interactions in a general class of such theories. The results indicate that φ4 interactions remain irrelevant in the percolation problem.

Description
Keywords
physics, condensed matter
Citation
Amit, D. J.; Wallace, D. J.; Zia, R. K. P., "Universality in the percolation problem—Anomalous dimensions of φ4 operators," Phys. Rev. B 15, 4657 DOI: http://dx.doi.org/10.1103/PhysRevB.15.4657