Nonasymptotic critical behavior from field theory at d=3 : The disordered-phase case

Abstract

The theoretical framework and the details of calculations of nonasymptotic critical behavior, above ${T}_{c}$, previously published for $n=1$, are presented and extended to the cases $n=2 \mathrm{and} 3$. The complete description of the real preasymptotic critical domain ${\mathcal{D}}_{\mathrm{preas}}$ needs only three adjustable parameters. We show that the ${\ensuremath{\varphi}}^{4}$ model at infinite cutoff is sufficient to obtain this description. The higher-transient and finite-cutoff effects in ${\mathcal{D}}_{\mathrm{preas}}$ affect only the adjustable parameters. A precise nonperturbative treatment of the ${\ensuremath{\varphi}}^{4}$ field theory exactly for $d=3$, in the spirit of the Parisi work, yields nonasymptotic functions of temperature which, including all the quantitative universal characteristics of the critical behavior in ${\mathcal{D}}_{\mathrm{preas}}$, are adapted to a suitable comparison with experiments. We emphasize that this work allows a determination, within the experimental accuracy, of the size of ${\mathcal{D}}_{\mathrm{preas}}$ and an appreciation of the effects of the higher corrections to scaling. We also give the estimates for $n=1, 2, \mathrm{and} 3$ of a new universal combination of amplitudes (${{R}_{B}}_{\mathrm{cr}}$) which concerns the specific heat alone.