It is widely claimed that quantum field theory (as many-body perturbation theory is commonly referred to) provides, via renormalization, fantastically precise predictions of experimental results, both in phase transitions and in particle physics. However the relevant series are notoriously divergent, so that Borel transformations are used to extract satisfactory results.
For phase transitions the commonly cited works are those of Zinn-Justin and coworkers, which however rely on several additional adjustable parameters. In his survey  Zinn-Justin states with crystalline openness: "rho is a free parameter, adjusted empirically to improve the convergence of the transformed series ... Eventually the method has been refined, which involves also introducing two additional free parameters. ... It is clear from these remarks that the errors quoted in the final results are educated guesses based on large numbers of consistency checks.". While quotes out of context can be deceptive, personally I am left with some doubts about the predictive character of the theory.
 Jean Zinn-Justin, Phase Transitions and Renormalization Group from Theory to Numbers, Séminaire Poincaré 2, 2002, 55-74 (link).