Critical Exponents in 3.99 Dimensions

Abstract

Critical exponents are calculated for dimension $d=4-\epsilon$ with $\epsilon$ small, using renormalization-group techniques. To order $\epsilon$ the exponent $\gamma$ is $1+\frac{1}{6}\epsilon$ for an Ising-like model and $1+\frac{1}{5}\epsilon$ for an $\mathrm{XY}$ model.