Six-loop renormalization group functions ofO(n)-symmetric ϕ⁶-theory and ϵ-expansions of tricritical exponents up to ϵ³

We present a six-loop calculation for Wilson's β-function and for the crossover exponent φ of the tricritical O(n) symmetric ϕ6 theory in d = 3 − dimensions. The counterterms of all but one of the 29 diagrams can be calculated analytically, while for one diagram high-precision numerical calculations together with the PSLQ integer relation search algorithm was used to come up with an analytical result. The divergences of the dimensionally regularized diagrams are removed by minimal subtraction.