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The obtention (up to five or six loop orders) of nonasymptotic critical behavior, above and below Tc, from the field theoretical framework is presented and discussed.When talking about critical behavior one usually thinks of critical exponents (power laws), and eventually of corrections to scaling, all notions strictly related to the unprecise definition of an asymptotic critical domain. In fact criticality may be observed beyond that theoretical domain and, sometimes, this makes it difficult to compare theory and experiments.[1] For example, it is thought that some systems could undergo a retarded crossover [2] from classical to Ising-like critical behaviors. In such a case, the critical domain would be much larger than for, say, pure fluids. Consequently many correctionto-scaling terms should be introduced and, it is very likely that the series would not converge. For that reason, nonasymptotic theoretical expressions of critical behaviors are required to describe such systems.It is not very well known that, beyond the estimations of the critical exponents, the renormalization group (RG) theory [3] is also adapted to provide us with nonasymptotic forms of the critical behavior especially when a crossover phenomenon occurs (the crossover is then characterized by the competition of two fixed points).We briefly present here the principles of the calculations done within the massive field theoretical framework in three dimensions (d = 3) [4] and which have yielded accurate nonasymptotic forms of the susceptibility χ(τ ) and the specific heat C(τ ) for τ = (T − T c )/T c > 0 and τ < 0, of the correlation length ξ(τ ) for τ > 0 and of the coexistence curve M(τ ) for τ < 0. [5,6] The calculations presented here have induced, directly or indirectly, several subsequent works. [7,8] We hope that this text will encourage further works on nonasymptotic critical behavior. We think, in particular, that the variational perturbation theory used recently to estimate universal exponents [9] and amplitude ratios, [10] could be an advantageous tool.Let us first specify the meaning of the title. "Nonasymptotic critical behavior" means that we perform a resummation of the infinite series of correction-to-scaling terms which are expected [11] in the asymptotic expression of any singular quantity such as ξ(τ ). Particularly, for τ → 0 +,− , we have:

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We test equivalences between different realisations of Wilson's renormalisation group by computing the leading, subleading, and anti-symmetric corrections-to-scaling exponents, and the full fixed point potential for the Ising universality class to leading order in a derivative expansion. We discuss our methods with a special emphasis on accuracy and reliability. We establish numerical equivalence of Wilson-Polchinski flows and optimised renormalisation group flows with an unprecedented accuracy in the scaling exponents. Our results are contrasted with high-accuracy findings from Dyson's hierarchical model, where a tiny but systematic difference in all scaling exponents is established. Further applications for our numerical methods are briefly indicated.Comment: 9 pages, 7 figures, comparison and discussion/conclusions sharpened, references adde