Compact analytical form for non-zeta terms in critical exponents at order 1/N^3

D. J. Broadhurst, A. V. Kotikov

We simplify, to a single integral of dilogarithms, the least tractable O(1/N^3) contribution to the large-N critical exponent $\eta$ of the non-linear sigma-model, and hence ${\varphi }^4$-the…