Universality, twisted fans, and the Ising φ4 model

We calculate critical exponents for the Ising ${\ensuremath{\varphi}}^{4}$ model using universality in the form of "twisted fans" previously introduced in the Reggeon field theory. The universality is with respect to scales induced through renormalization. Exact twists are obtained at $\ensuremath{\beta}=0$ in the one-loop calculation for dimension $D=2 \mathrm{and} 3$ with the correlation-length exponent $\ensuremath{\nu}=0.75 \mathrm{and} 0.60$ respectively. In the two-loop calculation we obtain $\ensuremath{\nu}\ensuremath{\approx}1.32 \mathrm{and} 0.68$. However, no twists are obtained for the propagator exponent $\ensuremath{\eta}$. The results for the standard two-loop calculations are also presented as functions of a scale.