Abstract
Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the specific heat may remain finite, and second, that near the critical point the entropy of the system, and therefore all free energies, do obey scaling. Although we limit ourselves to such a system, we elaborate about the possibilities of finding universality, as well as the precise values of the critical exponents using thermodynamics only.
Highlights
Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the specific heat may remain finite, and second, that near the critical point the entropy of the system, and all free energies, do obey scaling
renormalization group (RG) cannot be exaggerated, pervading the physics and chemistry of phase transitions and condensed matter in general, and influencing many other fields, from the emerging field of complex systems to high energy physics. As it is common knowledge, and expressed in too many articles and monographies, see e.g., Refs. [4,5,6,7], the scaling hypothesis has remained as such, namely as a hypothesis that leads to the equalities of the different critical exponents, and that its validation and the actual calculation of the exponents are the success of RG
The purpose of this article is to show that the scaling hypothesis follows directly from the laws of thermodynamics and the equilibrium conditions in a magnetic-like system with a coexistence curve of different thermodynamic states
Summary
Based on the foundations of thermodynamics and the equilibrium conditions for the coexistence of two phases in a magnetic Ising-like system, we show, first, that there is a critical point where the isothermal susceptibility diverges and the specific heat may remain finite, and second, that near the critical point the entropy of the system, and all free energies, do obey scaling. We show first that the existence of such a curve implies that there is a point, the critical point of the phase transition, where the thermodynamic properties may or may not be analytic, and where the isothermal susceptibility must diverge, while the specific heat may remain finite.
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