Abstract
We provide an introduction to the constructive results on interacting Fermions in two dimensions at thermal equilibrium above the critical temperature of pair condensation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Disertori and V. Rivasseau, Interacting Fermi liquid in two dimensions at finite temperature, Part I: Convergent Attributions, Commun. Math. Phys. 215, 251 (2000).
M. Disertori and V. Rivasseau, Interacting Fermi liquid in two dimensions at finite temperature, Part II: Renormalization, Commun. Math. Phys. 215, 291 (2000).
V. Rivasseau, The two dimensional Hubbard Model at half-filling: I. Convergent Contributions, Journ. Stat. Phys. 106, 693–722, (2002).
S. Afchain, J. Magnen and V. Rivasseau, Renormalization of the 2-point function of the Hubbard Model at half-filling, cond-mat/0409231 (2004), to appear in Annales Henri Poincaré.
S. Afchain, J. Magnen and V. Rivasseau, The Hubbard Model at half-filling, part III: the lower bound on the self-energy, cond-mat/0412401 (2004), to appear in Annales Henri Poincaré.
See e.g. E. Fradkin, “Field Theories of Condensed Matter Systems”, Frontiers in Physics, 1991.
M. Salmhofer, Continuous renormalization for Fermions and Fermi liquid theory, Commun. Math. Phys. 194, 249 (1998).
M. Salmhofer, Renormalization, an introduction, Springer Verlag, 1999.
G. Benfatto and G. Gallavotti, Renormalization Group, Physics Notes, Chap. 11 and references therein, Vol. 1 Princeton University Press, 1995
J. Feldman, J. Magnen, V. Rivasseau and E. Trubowitz, An Intrinsic 1/N Expansion for Many Fermion System, Europhys. Letters 24, 437 (1993).
P.W. Anderson, Luttinger liquid behavior of the normal metallic state of the 2D Hubbard model, Phys. Rev. Lett. 64 1839–1841 (1990).
Joel Feldman, H. Knörrer and E. Trubowitz, A two dimensional Fermi Liquid, series of papers in Commun. Math. Phys. 247, 1–319, 2004 and Reviews in Math. Physics, 15, 9, 949-1169, (2003).
G. Benfatto, A. Giuliani and V. Mastropietro, Low temperature Analysis of Two-Dimensional Fermi Systems with Symmetric Fermi surface, Ann. Henri Poincaré, 4 137, (2003).
M. Disertori, J. Magnen and V. Rivasseau, Interacting Fermi liquid in three dimensions at finite temperature, part I: Convergent Contributions, Ann. Henri Poincaré, 2 733–806 (2001).
A. Abdesselam and V. Rivasseau, Trees, Forests and Jungles: A Botanical Garden for Cluster Expansions, in “Constructive Physics”, LNP 446, Springer Verlag, 1995.
J.A. Bondy and U.S.R. Murty, Graph theory with applications, North-Holland Editions, 1979.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this chapter
Cite this chapter
Rivasseau, V. (2006). Interacting Fermions in 2 Dimensions. In: Asch, J., Joye, A. (eds) Mathematical Physics of Quantum Mechanics. Lecture Notes in Physics, vol 690. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34273-7_14
Download citation
DOI: https://doi.org/10.1007/3-540-34273-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31026-6
Online ISBN: 978-3-540-34273-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)