Abstract
The lattice gas system is studied. In frameworks of statistical mechanics, it is proposed the analytic algorithm of approximations construction when pressure calculating. Algorithm is built on the basis of virial expansion using special small parameter ν. The parameter is introduced by the prescription of the corresponding ν-power weight to each Mayer diagram without contact vertexes. The obtained formulas describe the gas-liquid phase transition. The density dependence on pressure has the jump if the temperature is less than the critical one. The algorithm permits to calculate the phase diagrams contained the critical point. The formula of pressure obtained at null approximation corresponds to the self-consistent field approximation. Corrections to the critical temperature, the density jump value and the curves of phase diagrams are calculated in the approximation with the accuracy to first order on ν. It is manifested the forbiddance of phase transition in one-dimensional system.
Highlights
Statistical theory of gas-liquid phase transition has the large history, but there is not a mathematically substantiated method in frames of statistical mechanics for calculation of the thermodynamic characteristics of the transition even for such simple systems of statistical physics as one-atom gases
In frameworks of statistical mechanics, it is proposed the analytic algorithm of approximations construction when pressure calculating
Corrections to the critical temperature, the density jump value and the curves of phase diagrams are calculated in the approximation with the accuracy to first order on ν
Summary
Statistical theory of gas-liquid phase transition has the large history, but there is not a mathematically substantiated method in frames of statistical mechanics for calculation of the thermodynamic characteristics of the transition even for such simple systems of statistical physics as one-atom gases In this communication we point out the way of problem solving. Published under licence by IOP Publishing Ltd of condensation [1] In these works the concrete mathematical mechanism has been proposed according to which singularities corresponding the gas-liquid phase transition are appeared. The presence of a first order phase transition in a lattice gas at sufficiently low temperatures is proved in the work [3] It is done under conditions when the attraction region of the interaction potential plays a dominant role. Result obtained in these works is analogous to zero approximation which is discussed in 5th section of our article
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