Abstract
The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q 1=+1) and negatively (q 2=−1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against collapse of positive-negative pairs of charges for the dimensionless coupling constant (inverse temperature) β<4. The mapping of the Coulomb gas is made onto the complex Bullough–Dodd model, and recent results about that integrable 2D field theory are used. The mapping provides the full thermodynamics (the free energy, the internal energy, the specific heat) and the large-distance asymptotics of the particle correlation functions, in the whole stability regime of the plasma. The results are checked by a small-β expansion and close to the collapse β=4 point. The comparison is made with the exactly solvable symmetric version of the model (q 1=+1,q 2=−1), and some fundamental changes in statistics caused by the charge asymmetry are pointed out.
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REFERENCES
E. H. Lieb, Rev. Mod. Phys. 48:553(1976).
J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6:1181(1973).
L. Blum, C. Gruber, J. L. Lebowitz, and P. Martin, Phys. Rev. Lett. 48:1769(1982).
A. Salzberg and S. Prager, J. Chem. Phys. 38:2587(1963).
R. M. May, Phys. Lett. A 25:282(1967).
E. H. Hauge and P. C. Hemmer, Phys. Norvegica 5:209(1971).
R. E. Prange and S. M. Girvin, The Quantum Hall Effect (Springer, New York, 1987).
P. Di Francesco, M. Gaudin, C. Itzykson, and F. Lesage, Int. J. Mod. Phys. A 9:4257(1994).
Ph. Choquard and J. Clérouin, Phys. Rev. Lett. 50:2086(1983).
M. A. Moore and A. Pérez-Garrido, Phys. Rev. Lett. 82:4078(1999).
B. Jancovici, Phys. Rev. Lett. 46:386(1981).
B. Jancovici, in Inhomogeneous Fluids, D. Henderson, ed. (Dekker, New York, 1992).
M. Gaudin, J. Phys. (France) 46:1027(1985).
F. Cornu and B. Jancovici, J. Stat. Phys. 49:33(1987).
F. Cornu and B. Jancovici, J. Chem. Phys. 90:2444(1989).
L. Šamaj and I. Travěnec, J. Stat. Phys. 101:713(2000).
L. Šamaj and B. Jancovici, J. Stat. Phys. 103:717(2001).
L. Šamaj, J. Stat. Phys. 103:737(2001).
L. Šamaj and B. Jancovici, J. Stat. Phys. 106:301(2002).
L. Šamaj and B. Jancovici, J. Stat. Phys. 106:323(2002).
J. P. Hansen and P. Viot, J. Stat. Phys. 38:823(1985).
L. Šamaj, Physica A 297:142(2001).
B. I. Shklovskii, Phys. Rev. E 60:5802(1999).
T. T. Nguyen, A. Y. Grosberg, and B. I. Shklovskii, Phys. Rev. Lett. 85:1568(2000).
R. Messina, C. Holm, and K. Kremer, Phys. Rev. E 64:021405(2001).
A. B. Schmidt, Physica A 293:21(2001).
P. A. Mattsson, Ph.D. thesis, hep-th/0111261.
R. K. Dodd and R. K. Bullough, Proc. R. Soc. London A 352:481(1977).
A. V. Zhiber and A. B. Shabat, Dok. Akad. Nauk SSSR 247:5(1979).
A. V. Mikhailov, M. A. Olshanetsky, and A. M. Prelomov, Commun. Math. Phys. 79:473(1981).
C. Deutsch and M. Lavaud, Phys. Rev. A 9:2598(1974).
B. Jancovici, P. Kalinay, and L. Šamaj, Physica A 279:260(2000).
F. H. Stillinger and R. Lovett, J. Chem. Phys. 49:1991(1968).
B. Jancovici, J. Stat. Phys. 17:357(1977).
P. Minnhagen, Rev. Mod. Phys. 59:1001(1987).
A. E. Arinshtein, V. A. Fateev, and A. B. Zamolodchikov, Phys. Lett. B 87:389(1979).
V. Fateev, S. Lukyanov, A. B. Zamolodchikov, and Al. B. Zamolodchikov, Nucl. Phys. B 516:652(1998).
Al. B. Zamolodchikov, Nucl. Phys. B 342:695(1990).
V. A. Fateev, Phys. Lett. B 324:45(1994).
S. Lukyanov and A. B. Zamolodchikov, Nucl. Phys. B 493:571(1997).
V. Fateev, S. Lukyanov, A. B. Zamolodchikov, and Al. B. Zamolodchikov, Phys. Lett. B 406:83(1997).
F. A. Smirnov, Int. J. Mod. Phys. A 6:1407(1991).
P. Baseilhac and M. Stanishkov, Nucl. Phys. B 612:373(2001).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products, 5th edn. (Academic Press, London, 1994).
F. A. Smirnov, Form-Factors in Completely Integrable Models of Quantum Field Theory (World Scientific, Singapore, 1992).
C. Acerbi, Nucl. Phys. B 497:589(1997).
V. Brazhnikov and S. Lukyanov, Nucl. Phys. B 512:616(1998).
N. V. Brilliantov, Contrib. Plasma Phys. 38:489(1998).
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Šamaj, L. Exact Solution of a Charge-Asymmetric Two-Dimensional Coulomb Gas. Journal of Statistical Physics 111, 261–290 (2003). https://doi.org/10.1023/A:1022209108732
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DOI: https://doi.org/10.1023/A:1022209108732