Estimate of the Critical Exponents from the Field-Theoretical Renormalization Group: Mathematical Sense of the "Standard Values"

Understand

New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series.

• The results almost coincide with the central values obtained by Le Guillou and Zinn-Justin (the so-called "standard values"), but have lower uncertainty.
• It has been shown that usual field-theoretical estimates implicitly imply the smoothness of the coefficient functions.
• The last assumption is open for discussion in view of the existence of the oscillating contribution to the coefficient functions.