Freezing transition in three and two dimensions by the generalized density functional theory

Details Freezing transition in three and two dimensions by the generalized density functional theory Freezing transition in three and two dimensions by the generalized density functional theory

1997-12-22

arxiv.org/abs/cond-mat/9712265v1

Physics

Condensed Matter

Statistical Mechanics

Lecture given on the International School on Strongly correlated systems and critical phenomena, held in JINR, Dubna (Russia)

Scientific paper

A brief introduction to conventional DFT of 3D freezing is given and some recent results are reviewed. The conventional DFT, however, can not be used in the 2D case, particularly, because it can not describe the hexatic phase -- intermediate phase of 2D melting. We generalize DFT to describe 2D systems and two-stage melting scenario including intermediate hexatic phase. Hexatic phase is characterized by the appearance of bond orientational ordering. Our approach describes this fact in terms of the appearance of nonisotropic part of the two-particle distribution function while one-particle density remains constant. Now we are dealing with the bifurcation of the solution of the equation for the binary distribution function. Microscopic expressions for elastic moduli and the Frank constant of hexatic phase are derived on the base of comparison of distribution functions asymptotic behavior with the results of phenomenological theories. We use our approach for the calculation of the phase boundary between usual isotropic liquid and hexatic phase and slightly modified traditional DFT for the phase boundary between hexatic phase and crystalline solid for a number of 2D systems (hard disks, classical electron crystal, thin superconducting films, Yukawa system etc.)

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