Fundamental Critical Relations

Abstract

We consider systems which exhibit typical critical dependence of the specific heat: <artwork name="GPHT31001ei1">) where γ, γ ′ are critical exponents (γ = α for <artwork name="GPHT31001ei2"> for <artwork name="GPHT31001ei3">), as well as, the case when <artwork name="GPHT31001ei4">, uniaxial ferroelectrics; a = 1, liquid He4). Starting from the critical behaviour of the specific heat we can exactly find the asymptotic form of the Gibbs (Helmholtz) potential in the vicinity of the critical point for each case separately. We derive in this way many exact critical relations in the limit T → TC which remain the same for each particular case. They define a new class of universal critical relations independent from the underlying microscopic mechanism and the symmetry of these systems. It, however, means that they are independent from the critical indices, characterizing each particular material. The derived relations are valid for magnetic, ferroelectric and superconducting materials, as well as, for liquid He4 and they have very important consequences concerning the mutual relations between critical amplitudes of many thermodynamical quantities near the critical point and therefore can be important and interesting from the experimental and technological point of view.