THE SCALE-INVARIANCE HYPOTHESIS IN THE CRITICAL-POINT THEORY

The analysis of well-known thermodynamic equations related to the crit ical point and established before the formulation of the scale invaria nce hypothesis reveals that the main results that follow from this hyp othesis do not differ from those contained in the thermodynamic equati ons mentioned above. Therefore, the scale invariance hypothesis does n ot contain any novelty with respect to the critical point. It is point ed out that the basic relationship between the critical indices, d nu = 2 beta + gamma, which expresses analytically the scale invariance hy pothesis, follows from the thermodynamic equations for the critical po int established before this hypothesis, and, as a consequence, may be extended to the phase transitions of the second kind. A new proof of t he equality nu = (d - 1), where nu is the critical index for the surfa ce tension, is also given.