Universality in the percolation problem—Anomalous dimensions of φ4 operators
Amit, D. J.
Wallace, D. J.
Zia, R. K. P.
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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.