How to Cite
Downloads
Most read articles by the same author(s)
- Robert Paul Salazar, Gabriel Téllez, Diego Felipe Jaramillo, Diego Luis González, Chaos in the Diamond-Shaped Billiard with Rounded Crown , Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. 39 No. 151 (2015)
Métricas Alternativas
Dimensions
Abstract
A review of two-dimensional exactly solvable models of statistical mechanics of Coulomb systems is presented. These are systems composed of charged particles. Two models are considered: the two-component plasma and the one-component plasma. Analogies between these classical systems and quantum field theories are exploited, which allow for an analytic resolution of the models. For the one-component plasma, new results for the free energy are presented.
Keywords
References
[Brydges, Martin 1999] D. C. Brydges and Ph. A. Martin, “Coulomb systems at low density: A review”, J. Stat. Phys. 96, 1163 (1999).
[Bernevig, Haldane 2008] B. A. Bernevig, F. D. M. Haldane, “Model fractional quantum Hall states and Jack polynomials”, Phys. Rev. Lett. 100, 246802 (2008).
[Bernevig, Regnault 2009] B. A. Bernevig, N. Regnault, “Anatomy of abelian and non-abelian fractional quantum Hall states”, Phys. Rev. Lett. 103 206801 (2009).
[Caillol 1981] J. M. Caillol, “Exact results for a two-dimensional one-component plasma on a sphere”, J. Physique – Lettres 42, L-245 (1982).
[Chapman 1913] D. L. Chapman, “A contribution to the theory of electrocapillarity”, Philos. Mag. 25 475 (1913).
[Coleman 1975] S. Coleman, “Quantum sine–Gordon equation as the massive Thirring model”, Phys. Rev. D 11, 2088 (1975).
[Cornu, Jancovici 1989] F. Cornu, B. Jancovici, “The electrical double layer: A solvable model”, J. Chem. Phys. 90, 2444
[Dashen, Hasslacher, Neveu, 1975] R. F. Dashen, B. Hasslacher, A. Neveu, “Particle spectrum in model field theories from semiclassical functional integral techniques”, Phys. Rev. D 11, 3424 (1975).
[Debye, H¨uckel 1923] P. Debye, E. H¨uckel, “The theory of electrolytes. I. Lowering of freezing point and related phenomena”, Phys. Z 24185 (1923).
[Ferrero, T´ellez 2007] A. Ferrero, G. T´ellez, “Two-dimensional two-component plasma with adsorbing impurities”, J. Stat. Phys. 129, 759(2007).
[Forrester 2010] P. J. Forrester, Log-Gases and Random Matrices, Princeton University Press (2010).
[Forrester, Jancovici, T´ellez 1996] P. J. Forrester, B. Jancovici, G. T´ellez, “Universality in some classical Coulomb systems”, J. Stat. Phys. 84, 359 (1996).
[Gaudin 1985] M. Gaudin, “L’isotherme critique d’un plasma sur r´eseau (β = 2, d = 2, n = 2)”, J. Phys. (France) 46, 1027
(1985).[Ginibre 1965] J. Ginibre, “Statistical ensembles of complex, quaternion, and real matrices”, J. Math. Phys. 6, 440 (1965).
[Gouy 1910] G. L. Gouy, “Sur la constitution de la charge ´electrique a la surface d’un ´electrolyte”, J. Phys. 9, 457 (1910).
[Jancovici 1981] B. Jancovici, “Exact results for the two-dimensional one-component plasma”, Phys. Rev. Lett. 46, 386 (1981).
[Jancovici, Manificat, Pisani 1994] B. Jancovici, G. Manificat, C. Pisani, “Coulomb systems seen as critical systems: Finite-size effects in two dimensions”, J. Stat. Phys. 76, 307(1994).
[Jancovici, T´ellez 1996] B. Jancovici, G. T´ellez, “Coulomb systems seen as critical systems: Ideal conductor boundaries” J. Stat. Phys. 82, 609 (1996).
[Jancovici, T´ellez 1998] B. Jancovici, G. T´ellez, “Twodimensional Coulomb systems on a surface of constant negative curvature”, J. Stat. Phys. 91, 953 (1998).
[Kalinay, ˇSamaj 2002] P. Kalinay, L. ˇSamaj, “Thermodynamic properties of the two-dimensional Coulomb gas in the low-density limit”, J. Stat. Phys. 106, 857 (2002).
[Klauder 2011] J. R. Klauder, A modern approach to functional integration, Springer (2011).
[Laughlin 1983] R.B. Laughlin, “Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations”, Phys. Rev. Lett. 50, 1395 (1983).
[Lieb, Lebowitz 1972] E. H. Lieb, J. L. Lebowitz, “The constitution of matter: Existence of thermodynamics for systems composed of electrons and nuclei”, Adv. Math. 9, 316 (1972).
[Macdonald 1995] I. G. Macdonald, Hall polynomials and symmetric functions, 2nd ed., Oxford University Press, (1995).
[McCaskill, Fackerell 1988] J. S. McCaskill, E. D. Fackerell, “Painlev´e solution of the Poisson-Boltzmann equation for a cylindrical polyelectrolyte in excess salt solution”, J. Chem. Soc. Faraday Trans. 2, 161 (1988).
[McCoy, Tracy, Wu 1977] B. M. McCoy, C. A. Tracy, T. T. Wu, “Painlev´e functions of the third kind”, J. Math. Phys. 18, 1058 (1977).
[Mehta 1991] M. L. Mehta, Random Matrices, Academic Press, 2nd ed. (1991).
[Onsager 1944] L. Onsager, “Crystal statistics. I. A twodimensional model with an order-disorder transition”, Phys. Rev. 65, 117 (1944).
[ˇSamaj 2003] L. ˇSamaj, “Exact solution of a charge-asymmetric two-dimensional Coulomb gas”, J. Stat. Phys. 111, 261(2003).
[ˇSamaj 2004] L. ˇSamaj, “Is the two-dimensional one-component plasma exactly solvable?”, J. Stat. Phys. 117, 131 (2004).
[ˇSamaj, Jancovici 2002] L. ˇSamaj, B. Jancovici, “Largedistance behavior of particle correlations in the two dimensional two-component plasma”, J. Stat. Phys. 106, 301(2002).
[ˇSamaj, Percus 1995] L. ˇSamaj, J. K. Percus, “A functional relation among the pair correlations of the two-dimensional one-component plasma”, J. Stat. Phys. 80, 811 (1995).
[ˇSamaj, Travˇenec 2000] L. ˇSamaj, I. Travˇenec, “Thermodynamic properties of the two-dimensional two-component plasma”, J. Stat. Phys. 101, 713 (2000).
[Samuel 1978] S. Samuel, “Grand partition function in field theory with applications to sine–Gordon field theory”, Phys. Rev. D 18 1916 (1978).
[T´ellez 1997] G. T´ellez, “Two-component plasma in a gravitational field”, J. Chem. Phys. 106, 8572 (1997).
[T´ellez 2005] G. T´ellez, “Short-distance expansion of correlation functions for charge-symmetric two-dimensional two-component plasma: Exact results”, J. Stat. Mech. : Theory and Experiment, P10001 (2005)
[T´ellez 2006] G. T´ellez, “Charge inversion of colloids in an exactly solvable model”, Europhys. Lett. 76, 1186 (2006).
[T´ellez 2007] G. T´ellez, “Equation of state in the fugacity format for the two-dimensional Coulomb gas”, J. Stat. Phys. 126, 281 (2007).
[T´ellez, Forrester 1999] G. T´ellez, P. J. Forrester, “Exact finite size study of the 2dOCP at Γ = 4 and Γ = 6”, J. Stat. Phys. 97, 489 (1999).
[T´ellez, Forrester 2012] G. T´ellez, P. J. Forrester, “Expanded Vandermonde powers and sum rules for the two-dimensional one-component plasma”, J. Stat. Phys. 148, 824 (2012).
[T´ellez, Merch´an 2002] G. T´ellez, L. Merch´an, “Solvable model for electrolytic soap films: the two-dimensional two-component plasma”, J. Stat. Phys. 108, 495 (2002).
[T´ellez, Trizac 2006] G. T´ellez, E. Trizac, “Exact asymptotic expansions for the cylindrical Poisson-Boltzmann equation”, J. Stat. Mech. P06018 (2006).
[Torres, T´ellez 2004] A. Torres, G. T´ellez, “Finite-size corrections for Coulomb systems in the Debye-Huckel regime”, J. Phys. A: Math. and Gen. 37, 2121 (2004).
[Tracy, Widom 1998] C. A. Tracy, and H. Widom, “Asymptotics of a class of solutions to the cylindrical Toda equations”, Comm. Math. Phys. 190, 697 (1998).
[Tracy, Widom 1997] C A. Tracy, H. Widom, “On exact solutions to the cylindrical Poisson-Boltzmann equation with applications to polyelectrolytes”, Physica A 244, 402 (1997).
[Trizac, T´ellez 2006] E. Trizac, G. T´ellez, “Onsager-Manning Oosawa condensation phenomenon and the effect of salt”, Phys. Rev. Lett. 96, 038302 (2006).
[Trizac, T´ellez 2007] E. Trizac, G. T´ellez, “Preferential interaction coefficient for nucleic acids and other cylindrical polyions”, Macromolecules 40 (4), 1305 (2007).
[Verwey, Overbeek 1948] E. J. W. Verwey, J. T. G. Overbeek Theory of the stability of lyophobic colloids, Elsevier (1948).
[Widom 1997] H. Widom, “Some classes of solutions to the Toda lattice hierarchy”, Comm. Math. Phys. 184, 653 (1997). 84, 161 (1988).
[Zamolodchikov 1995] Al. B. Zamolodchikov, “Mass scale in the sin–Gordon model and its reductions”, Int. J. Mod. Phys. A 10, 1125 (1995).
[Zamolodchikov 1979] A. B. Zamolodchikov, Al. B. Zamolod-chikov, “Factorized S-matrices in two dimensions as the exact solutions of certain relativistic quantum field theory models”, Ann. Phys. 120, 253 (1979)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Copyright (c) 2023 Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales