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Based on the foundations of thermodynamics and the equilibrium conditions forthe coexistence of two phases in a magnetic Ising-like system, we show, first,that there is a critical point where the isothermal susceptibility diverges andthe specific heat may remain finite, and second, that near the critical pointthe entropy of the system, and therefore all free energies, do obey scaling.Although we limit ourselves to such a system, we elaborate about thepossibilities of finding universality, as well as the precise values of thecritical exponents using thermodynamics only.

Derivation of the critical point scaling hypothesis using thermodynamics only