Bounds for the Hubbard Model Free Energy: Numeric Aspects
Department for Mathematical Methods in Physics
Faculty of Physics, University of Warsaw
ul. Hoża 74, 00-682 Warszawa, Poland
e-mail: wjacek@fuw.edu.pl
Received:
Received: 23 March 2010; accepted: 8 July 2010; published online: 20 September 2010
DOI: 10.12921/cmst.2010.16.02.207-210
Abstract:
In the paper [1], series of upper bounds and two lower ones for the partition function of the Hubbard model have been derived. The numerical values of upper and lower approximants have also been calculated for small systems for U > 0 case. Here the numeric examination of bounds is continued: the temperature behaviour of approximants is studied and the U < 0 case is considered.
Key words:
exact diagonalization study, Falicov-Kimball model, Hubbard model
References:
[1] J. Wojtkiewicz, J. Stat. Phys. 135, 375 (2009).
[2] J. Hubbard, Proc. Roy. Soc. London A 276, 238 (1963).
[3] L.M. Falicov, J.C. Kimball, Phys. Rev. Lett. 22, 997 (1969).
[4] C. Gruber, N. Macris, Helv. Phys. Acta 69, 851 (1996).
[5] S. Golden, Phys. Rev. 137 B, 1127 (1965).
[6] C.J. Thompson, J. Math. Phys. 6, 1812 (1965).
[7] B. Simon, The statistical mechanics of lattice gases, vol. 1.
Princeton University Press, Princeton, New Jersey (1993).
[8] W.H. Press, S.T. Teukolsky, W.T. Vetterling, B.P. Flannery,
Numerical Recipes in C++, Cambridge University Press (2007).
[9] M.E. Fisher, J. Chern. Phys. 42, 3852 (1965).
[10] R. Valenti, C. Gros, P.J. Hirschfeld, W. Stephan, Phys. Rev. B 44, 13203 (1991).
[11] R. Valenti, J. Stolze, P.J. Hirschfeld, Phys. Rev. B 43, 13743 (1991).
[12] E.W. Carlson, V.J. Emery, S.A. Kivelson, D. Organd, condmat/0206217.
In the paper [1], series of upper bounds and two lower ones for the partition function of the Hubbard model have been derived. The numerical values of upper and lower approximants have also been calculated for small systems for U > 0 case. Here the numeric examination of bounds is continued: the temperature behaviour of approximants is studied and the U < 0 case is considered.
Key words:
exact diagonalization study, Falicov-Kimball model, Hubbard model
References:
[1] J. Wojtkiewicz, J. Stat. Phys. 135, 375 (2009).
[2] J. Hubbard, Proc. Roy. Soc. London A 276, 238 (1963).
[3] L.M. Falicov, J.C. Kimball, Phys. Rev. Lett. 22, 997 (1969).
[4] C. Gruber, N. Macris, Helv. Phys. Acta 69, 851 (1996).
[5] S. Golden, Phys. Rev. 137 B, 1127 (1965).
[6] C.J. Thompson, J. Math. Phys. 6, 1812 (1965).
[7] B. Simon, The statistical mechanics of lattice gases, vol. 1.
Princeton University Press, Princeton, New Jersey (1993).
[8] W.H. Press, S.T. Teukolsky, W.T. Vetterling, B.P. Flannery,
Numerical Recipes in C++, Cambridge University Press (2007).
[9] M.E. Fisher, J. Chern. Phys. 42, 3852 (1965).
[10] R. Valenti, C. Gros, P.J. Hirschfeld, W. Stephan, Phys. Rev. B 44, 13203 (1991).
[11] R. Valenti, J. Stolze, P.J. Hirschfeld, Phys. Rev. B 43, 13743 (1991).
[12] E.W. Carlson, V.J. Emery, S.A. Kivelson, D. Organd, condmat/0206217.
