The epsilon expansion near absolute zero

Abstract

Epsilon expansion is an important part of the renormalization group approach; it allows substantiating the scaling paradigm and is used in the modern theory of critical phenomena. It is shown that at a critical temperature equal to zero, the expression for the critical heat capacity exponent already in the first order in epsilon d − = 4 – (d – is the dimension of space) changes its form. This, however, does not indicate a violation of the scaling approach, although the classical Essam-Fisher equation also changes, as does the Rushbrook inequality. The generalized Essam-Fisher interpolation equality and the generalized Rushbrook inequality are given, which are valid for any value of the critical temperature, in particular, for the critical temperature equal to zero. The generalized relations are consistent with the renormalization-group approach, - expansion and scaling paradigm. The fluctuations are considered to be classical (thermodynamic), the conditions are determined when this takes place.