Estimation of critical exponents from cluster coefficients and the application of this estimation to hard spheres

DOI10.1073/PNAS.0700778104zbMATH Open1155.82007arXivcond-mat/0603520OpenAlexW2124311779WikidataQ35749491 ScholiaQ35749491MaRDI QIDQ5385915

Asher Baram, E. Eisenberg

Publication date: 7 May 2008

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Abstract: For a large class of repulsive interaction models, the Mayer cluster integrals can be transformed into a tridiagonal symmetric matrix, whose elements converge to a constant with a 1/n^2 correction. We find exact expressions, in terms of these correction terms, for the two critical exponents describing the density near the two singular termination points of the fluid phase. We apply the method to the hard-spheres model and find that the metastable fluid phase terminates at rho_t=0.751(5). The density near the transition is given by (rho_t-rho)~(z_t-z)^sigma', where the critical exponent is predicted to be sigma'=0.0877(25). The termination density is close to the observed glass transition, and thus the above critical behavior is expected to characterize the onset of glassy behavior in hard spheres.

Full work available at URL: https://arxiv.org/abs/cond-mat/0603520

Mathematics Subject Classification ID

Critical phenomena in equilibrium statistical mechanics (82B27)

Cites Work

• On the universality of the nonphase transition singularity in hard- particle systems
• Ninth and tenth order virial coefficients for hard spheres in \(D\) dimensions

Related Items (3)

Ninth and tenth order virial coefficients for hard spheres in \(D\) dimensions ⋮ Backward clusters, hierarchy and wild sums for a hard sphere system in a low-density regime ⋮ Calculation of the number of collective degrees of freedom and of the admissible cluster size for isotherms in the Van-der-Waals model in supercritical states

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