Local theory of first-order phase transitions and critical phenomena

Two mechanisms of stability loss at the interphase boundary are possible. T he mechanism related to instability toward large-size fluctuations is respo nsible for liquid-vapor equilibria. The other mechanism, which involves sta bility loss at small distances, governs crystallization of liquids. The Orn stein-Zernike equation:is used to construct a theory of critical phenomena that does not use the similarity hypothesis, block Hamiltonians, and renorm alization group equations. This theory, nevertheless, leads to the same res ults as the classical theory of critical phenomena. The suggested theory is used to formulate criteria for determining the boundaries of the region of giant fluctuations, which is directly adjacent to the critical point, and of the whole critical region. An attempt is made to analyze the equation of state in the critical region.