Spatial correlations and the order parameter

He used to give blessings on Sundays and often punishments already on Mondays. 

Let us consider now behaviour of the gas-liquid system near the critical point. It reveals rather interesting effect called the critical opalescence, that is strong increase of the light scattering. Its analogs are known also in other physical systems in the vicinity of phase transitions. In the beginning of our century Einstein and Smoluchowski expressed an idea, that the opalescence phenomenon is related to the density (order parameter) fluctuations in the system. More consistent theory was presented later by Omstein and Zemike [23], who for the first time introduced a concept of the intermediate order as the spatial correlation in the density fluctuations. Later Zemike [24] has applied this idea to the lattice systems. 

As it is known [5], the intensity of the scattered light gives us cui information about the system s disorder, e.g., presence therein of pores, impurities etc. Since macroscopically liquid is homogeneous, critical opalescence arises due to local microscopic inhomogeneities - an appearance of small domains with different local densities. In other words, liquid is ordered inside these domains but still disorded on the whole since domains are randomly distributed in size and space, they appear and disappear by chance. Fluctuations of the order parameter have large amplitude and involve a wide spectmm of the wavelengths (which results in the milk colour of the scattered light). 

It should be reminded, that in gases under low pressure the correlation function is defined practically by the Boltzmann factor x( ) = exp -U r)/ kQT)). At high densities the potential U r) should be replaced 

The existence of the correlation length gives a proof to the hypothesis of the scale invariance [8, 9] in the vicinity of the critical point physical 

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