Abstract
The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionP L (ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities <ρ>. Particular attention is paid to the question whether accurate estimates of critical temperatureT c and critical density ρ c can be obtained. In the lattice gas model these critical parameters are known exactly and the limitations of the approach can thus be definitively asserted. The final estimates for the Lennard Jones problem areT c =0.47±0.01 (in units of the Lennard Jones energy ε) and ρ c (in units of σ2), a comparison with previous estimates is made.
Similar content being viewed by others
References
For a recent review, see Levesque, D., Weis, J.J.: In: The Monte Carlo method im condensed matter physics. Binder, K. (ed.), p. 121, Berlin, Heidelberg, New York, Tokyo: Springer 1992
Stanley, H.E.: An introduction to phase transitions and critical phenomena. Oxford: Oxford University Press 1971
Binder, K., Heermann, D.W.: Monte Carlo simulation in statistical physics: an introduction. Berlin, Heidelberg, New York: Springer 1988
Panagiotopoulos, A.Z.: Mol. Phys.61, 813 (1987)
Panagiotopoulos, A.Z., Quirke, N., Stapleton, M., Tildesley, D.: Mol. Phys.63, 527 (1988)
Smit, B., de Smedt, Ph., Frenkel, D.: Mol. Phys.68, 931 (1989)
Smit, B., Frenkel, D.: Mol. Phys.68, 951 (1989)
Smit, B., Frenkel, D.: J. Chem. Phys.94, 5663 (1991)
For a recent review of the Gibbs ensemble and additional references, see: Panagiotopoulos, A.Z.: Mol. Simulation9, 1 (1992)
Rovere, M., Heermann, D.W., Binder, K.: J. Phys.: Condensed Matter2, 7009 (1990)
Marx, D., Nielaba, P., Binder, K.: Phys. Rev. Lett.67, 3124 (1991)
Bruce, A.D., Wilding, N.B.: Phys. Rev. Lett.68, 193 (1992); Wilding, N.B., Bruce, A.D.: J. Phys. Condensed Matter4, 3087 (1992)
Mon, K.K., Binder, K.: J. Chem. Phys.96, 6989 (1992)
Onsager, L.: Phys. Rev.65, 117 (1944); Yang, C.N.: Phys. Rev.85, 808 (1952)
Binder, K.: Z. Phys. B—Condensed Matter43, 119 (1981)
Kaski, K., Binder, K., Gunton, J.D.: Phys. Rev. B29, 3996 (1984)
Landau, L.D., Lifshitz, E.M.: Statistical physics. 3rd edn., part 1. Oxford: Pergamon Press 1980
Privman, V. (ed): Finite size scaling and numerical simulation of statistical systems. Singapore: World Scientific 1990
Binder, K.: Wang, J.-S.: J. Stat. Phys.55, 87 (1989)
Domb, C.: In: Phase transition and critical phenomena. Vol. 3. London: Academic Press 1974
Baker, G.A.: Phys. Rev.124, 768 (1961)
Fisher, M.E., Burford, R.J.: Phys. Rev.156, 583 (1967)
Rovere, M., Heermann, D.W., Binder, K.: Europhys. Lett.6, 585 (1988)
Ercolessi, F.: Private communication (unpublished); for general reference see Allen, M.P., Tildesley, D.J.: Computer simulation of liquids. Oxford: Clarendon Press 1990
Singh, R.R., Pitzen, K.S., DePablo, J.J., Prausnitz, J.M.: J. Chem. Phys.92, 5463 (1990)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rovere, M., Nielaba, P. & Binder, K. Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis. Z. Physik B - Condensed Matter 90, 215–228 (1993). https://doi.org/10.1007/BF02198158
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02198158