Abstract
The thermodynamics of a 1—d fermion system can be perfectly mapped onto the thermodynamics of a two-component classical real gas on the surface of a cylinder. The latter system is studied by a modified Mayer cluster expansion method (Debye-Hückel theory and corrections to it). Simple reinterpretation of thermodynamic variables then leads to an exponentially activated behavior of the fermions' specific heat (spin density contribution). The exponent in Luther's recent gap formula is obtained as well as Zittartz's structure of the ground state energy. The method is applied to the case of strongly attractive spin-non-flip coupling (−1<γ ∥<−3/5) when the spin-flip couplingγ ⊥ is small. For largeγ ⊥ there is a gap everywhere.
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References
=LE, Luther, A., Emery, V.J.: Phys. Rev. Lett.33, 589 (1974)
Zittartz, J.: Z. Physik B23, 277 (1976)
=ES, Everts, H.U., Schulz, H.: Z. Physik B22, 285 (1975)
Gutfreund, H., Klemm, R.A.: Phys. Rev. B14, 1073 (1976)
Schlottmann, P. (to be published)
Sólyom, J.: J. Low Temp. Phys.12, 547 (1973)
Lee, P.A.: Phys. Rev. Lett.34, 1247 (1975)
Luther, A., Peschel, I.: Phys. Rev. B12, 3908 (1975)
Johnson, J.D., Krinsky, S., McCoy, B.: Phys. Rev. A8, 2526 (1973)
Luther, A.: Phys. Rev. B14, 2153 (1976); Phys. Rev. B (to be published)
Everts, H.U.: private communications
Chui, S.T., Lee, P.A.: Phys. Rev. Lett.35, 315 (1975)
Hauge, E.H., Hemmer, P.C.: Physica Norvegica5, 209 (1971)
Friedman, H.L.: Ionic Solution Theory. New York: Interscience 1962
Lenard, A.: J. Math. Phys.2, 682 (1961)
Mattis, D.C., Lieb, E.H.: J. Math. Phys.6, 304 (1965)
Luther, A., Peschel, I.: Phys. Rev. B9, 2911 (1974); Certain doubts in the bosonization procedure can be dispelled (H. Schulz, unpublished)
Schotte, K.D.: Z. Physik230, 99 (1970)
Zittartz, J.: private communications
Zittartz, J., Huberman, B.A.: Solid State Comm.18, 1373 (1976)
Tables of Integral Transforms (Bateman Manuscript Project) edited by A. Erdelyi. New York: McGraw-Hill 1954
Abrikosov, A.A., Gorkov, L.P., Dzyaloshinskii, I.E.: Methods of Quantum Field Theory in Statistical Physics, § 36.2. New Jersey: Prentice-Hall 1963
Zittartz, J.: Z. Physik B23, 55 (1976)
Everts, H.U., Koch, W. (to be published)
Abromowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. New York: Dover Publications 1970
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Schulz, H. Thermodynamics of a 1—d fermion system by cluster expansions. Z Physik B 26, 377–388 (1977). https://doi.org/10.1007/BF01570748
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DOI: https://doi.org/10.1007/BF01570748