Abstract
The two-dimensional, two-component plasma is considered in doubly periodic boundary conditions with the positive and negative charges confined to separate interlacing rectangular lattices. It is shown that at the special couplingΓ=2, on a lattice of 2M 1×2M 2 sites, the grand partition function can be written as a double integral over a product of determinants of dimension 2M 2×2M 2. On the basis of a conjecture regarding the zero distribution of the grand partition function, the large-M 2 behavior of the determinant is given and the pressure evaluated exactly.
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References
J. M. Kosterlitz and D. J. Thouless,J. Phys. C 6:1181 (1973).
D. R. Nelson, inPhase Transitions and Critical Phenomena, Vol. 7, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York).
P. Minnhagen,Rev. Mod. Phys. 59:1001 (1987).
J. Villain, inOrdering in Strongly Fluctuating Condensed Matter Systems, T. Riste, ed. (Plenum, New York, 1980), p. 221.
B. Neinhuis, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York).
J. Zittartz,Z. Phys. B 23:55 (1976).
C. N. Yang and T. D. Lee,Phys. Rev. 87:404 (1952).
C. Gallavoti and F. Nicoló,J. Stat. Phys. 39:133 (1985).
P. J. Forrester,J. Stat. Phys., to appear.
P. J. Forrester,J. Stat. Phys. 51:457 (1988).
M. Gaudin,J. Phys. (Paris)46:1027 (1985).
J. W. Perram and S. W. de Leeuw,Physica 109A:237 (1981).
M. L. Glasser,J. Math. Phys. 15:188 (1974).
J. D. Fay,Lecture Notes in Mathematics, No. 352 (1973).
P. J. Forrester,SIAM J. Math. Anal. 21:270 (1990).
F. Cornu and B. Jancovici,J. Stat. Phys. 49:33 (1987).
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Forrester, P.J. Exact results for the two-dimensional, two-component plasma atΓ=2 in doubly periodic boundary conditions. J Stat Phys 61, 1141–1160 (1990). https://doi.org/10.1007/BF01014369
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DOI: https://doi.org/10.1007/BF01014369