Virginia TechAmit, D. J.Wallace, D. J.Zia, Royce K. P.2014-05-072014-05-071977-05Amit, 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.15.46570163-1829http://hdl.handle.net/10919/47907We 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.application/pdfenIn Copyrightphysics, condensed matterArticle - Refereedhttp://journals.aps.org/prb/abstract/10.1103/PhysRevB.15.4657https://doi.org/10.1103/PhysRevB.15.4657