The nature of the rectilinear diameter singularity

Details The nature of the rectilinear diameter singularity The nature of the rectilinear diameter singularity

2007-03-17

arxiv.org/abs/cond-mat/0703459v2

Physica A: Statistical Mechanics and its Applications 388 (2009) pp. 621-627

Physics

Condensed Matter

Statistical Mechanics

6 pages, 1 figure

Scientific paper

10.1016/j.physa.2008.11.014

The rigorous explanation for the term $| t |^{2\beta}$ in the rectilinear diameter equation is given ($t = (T_c-T)/T_c$, $\beta$ is the critical exponent for the asymptotic form of the equation of state). The optimal order parameter, for which the branches of binodal are symmetric is constructed within the canonical formalism. It is shown that the ratio of the amplitudes $\f{D_{2\beta}}{D_{1-\alpha}}$ before $|t|^{2\beta}$ and $|t|^{1-\alpha}$ where $\alpha$ determines the behavior of the heat capacity, takes the universal character. The analysis of entropy for argon and water leads to $\beta = 0.33$ and $\f{D_{2-\beta}}{{D_{1-\alpha}}}\approx - 3.5$.

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