Diagrammatic renormalization-group method

A method is presented for the convergent evaluation of the Feynman diagrams for the free energy of an Ising-type system. The method involves three first-order Wilson-type differential equations whose solution near and at the fixed point yield the critical parameters $y$ and $\eta$. The method is discussed only for a system with no long-range order. That is, we consider only the case $H=0\mathrm{}$, $T>\mathrm{}{T}_c$. The $\epsilon$ expansions for $y$ and $\eta$ are evaluated to second order, and $y$ and $\eta$ are found exactly for the spherical model.