Abstract
The following is a brief description of Elliott Lieb’s papers on Condensed Matter Physics and on Exactly Soluble Models. The numbers refer to the publication list of Elliott Lieb, which appears at the end of this volume. Some of the papers that are not included in this volume Condensed Matter Physics and Exactly Soluble Models appear in the other Selectas of Elliott Lieb, namely The Stability of Matter: From Atoms to Stars,Inequalities, and Statistical Mechanics. The publication list shows which papers appear in which Selecta. The papers in this Selecta are additionally marked in boldface with their numbers as given in the table of contents. The numbers in square brackets refer to works by other authors, which are listed at the end of this survey.
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References
R.J. Baxter, Exactly Solved Models in Statistical Mechanics, Academic Press, New York, 1982.
M. Donsker, S.R.S. Varadhan, Asymptotic evaluation of certain Markov process expectations for large times. IV., Comm. Pure Appl. Math. 36 (1983), 183-212; Asymptotics for the polaron, Commun. Pure Appl. Math. 36 (1983), 505 - 528.
F.J. Dyson, Ground-State Energy of a Hard-Sphere Gas, Phys. Rev. 106 (1957), 20 - 26.
F.J. Dyson, Ground-state Energy of a Finite System of Charged Particles, J. Math. Phys. 8 (1967), 1538 - 1545.
F.J. Dyson, Missed opportunities, Bull. Am. Math Soc. 78 (1972), 635 - 652.
M. Fames, B. Nachtergaele, R.F. Werner, Finitely Correlated States on Quantum Spin Chains, Commun. Math. Phys. 144 (1992), 443 - 490.
R.P. Feynman, Slow electrons in a polar crystal,Phys. Rev. 97 (1955), 660-665.
L.L. Foldy, Charged boson gas, Phys. Rev. 124 (1961), 649 - 651, Errata: Phys. Rev. 125 (1962), 2208.
K. Fredenhagen, K.-H. Rehren, B. Schroer, Superselection sectors with braid group statistics and exchange algebras. I. General theory, Comm. Math. Phys. 125 (1989), 201 - 226.
I.B. Frenkel, M.G. Khovanov, Canonical bases in tensor products and graphical calculus for U q (sl2), Duke Math. J. 87 (1997), 409 - 480.
H. Fröhlich, Theory of Electrical Breakdown in Ionic Crystals, Proc. Roy. Soc. 160 (1937), 230 - 241.
H. Fröhlich, On the theory of superconductivity: the one-dimensional case, Proc. R. Soc. London Ser. A 223 (1954), 296 - 305.
M. GaudinUn système a une dimension de fermions en interaction,Phys. Lett. 24A (1967), 55-56.
P.S. GoldbaumExistence of Solutions to the Bethe Ansatz Equations for the ID Hubbard Model on a Finite Lattice. arXiv:cond-mat/0403736.
F.D.M. Haldane, Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O (3) nonlinear sigma model, Phys. Lett. 93A (1983), 464 - 468.
A.G. Izergin, Partition function of the six-vertex model in a finite volume, Soy. Phys. Dokl. 32 (1987), 878 - 879.
H. Jones, Applications of the Bloch Theory to the Study of Alloys and of the Properties of Bismuth, Proc. R. Soc. London Ser. A 147 (1934), 396 - 417.
V.F.R. Jones, Index for subfactors, Invent. Math. 72 (1983), 1 - 25.
V.F.R. Jones, A polynomial invariant for knots via von Neumann algebras, Bull. Amer. Math. Soc. (N.S.) 12 1985, 103 - 111.
R.W. Kasteleyn, Dimer statistics and phase transitions, J. Math. Phys. 4 (1963), 287 - 293.
L.H. Kauffman, S.L. Lins, Temperley-Lieb recoupling theory and invariants of 3-manifolds, Annals of Mathematics Studies, 134, Princeton University Press, Princeton, NJ, 1994.
B. Kaufman, Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis, Phys. Rev. 76 (1949), 1232 - 1243.
B. Kaufman, L. Onsager, Crystal Statistics. III. Short-Range Order in a Binary Ising Lattice, Phys. Rev. 76 (1949), 1244 - 1252.
V. Korepin, Calculation of Norms of Bethe Wave Functions, Commun. Math. Phys. 86 (1982), 391 - 418.
G. Kuperberg, Another proof of the Alternating-Sign Matrix Conjecture, Internat. Math. Res. Notices, 1996 (1996), 139 - 150.
G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, Ann. Math, 156 (2002), 835 - 866.
L.D. Landau, Electron motion in crystal lattices, Phys. Z. Sowjet 3 (1933), 664 - 665.
T.D. Lee, K. Huang, C.N. Yang, Eigenvalues and eigenfunctions of a Bose system of hard spheres and its low-temperature properties, Phys. Rev. 106 (1957), 1135 - 1145.
T.D. Lee, F. Low and D. Pines, The motion of slow electrons in a polar crystal, Phys. Rev. 90 (1953), 297 - 302.
J.M. Luttinger, An exactly soluble model of a many-fermion system, J. Math. Phys. 4 (1963), 1154 - 1162.
N. Macris, B. Nachtergaele, On the Flux Phase Conjecture at Half-Filling: An Improved Proof J. Stat. Phys. 85 (1996), 745 - 761.
J.B. McGuire, Interacting fermions in one dimension. I. Repulsive potential, J. Math. Phys. 6 (1965), 432 - 439.
W.H. Mills, D.P. Robbins, H. Rumsey, Alternating sign matrices and descending plane partitions, J. Combin. Theory, Ser. A 34 (1983), 340 - 359.
J.F. Nagle, Lattice statistics of hydrogen bonded crystals. I. The residual entropy of ice, J. Math. Phys. 7 (1966), 1484 - 1491.
L. Onsager, Crystal statistics. I. A two-dimensional model with an order-disorder transition, Phys. Rev. 65 (1944), 117 - 149.
L. Pauling, The structure and entropy of ice and of other crystals with some randomness of atomic arrangement,J. Am. Chem. Soc. 57 (1935), 26802684.
R.E. Peierls, Quantum Theory of Solids, Clarendon, Oxford, 1995, p. 108.
R.E. Peierls, Surprises in theoretical physics, Princeton University Press, 1979.
S.I. Pekar, Untersuchung über die Elektronentheorie der Kristalle, Akademie Verlag, Berlin, 1954.
M. Schick, Two-Dimensional System of Hard Core Bosons, Phys. Rev. A 3 (1971), 1067 - 1073.
B. Sutherland, Exact solution of a two-dimensional model for hydrogen-bonded crystals, Phys. Rev. Lett. 19 (1997), 103 - 104.
H.N.V. Temperley, Two-dimensional Ising models, in C. Domb, M.S. Green, Phase Transitions and Critical Phenomena, Vol. 1, Academic Press, 1972.
H.N.V. Temperley, M.E. Fisher, Dimer problem in statistical mechanics — an exact result, Philos. Mag. 6 (1961), 1061 - 1063.
W.E. Thirring, A solvable relativistic field theory. Ann. Phys. 3 (1958), 91112.
S. Tomonaga, Remarks on Bloch's method of sound waves applied to many-Fermion problems, Progress Theor. Phys. (Kyoto), 5 (1950), 544 - 569.
C.N. Yang, Some exact results for the many-body problem in one dimension with repulsive delta function interaction,Phys. Rev. Lett. 19 (1967), 1312-1315.
D. Zeilberger, Proof of the alternating sign matrix conjecture, Elec. J. Combin. 3 (2) (1996), R13.
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Nachtergaele, B., Solovej, J.P., Yngvason, J. (2004). A Survey by the Editors. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Condensed Matter Physics and Exactly Soluble Models. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06390-3_1
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