J. Phys. Soc. Jpn. 66 (1997) pp. 988-994  |Next Article|  |Table of Contents|
|Full Text PDF (904K)| |Buy This Article|

Low–Temperature Expansions and the Euler–Maclaurin Formula

Hideyuki Mizuta and Miki Wadati

(Received September 17, 1996)

Thermodynamic quantities of solvable models such as one–dimensional Heisenberg model can be obtained through the finite temperature Baxter formula. For the low–temperature expansions, the estimate of the finite size corrections by use of the Euler–Maclaurin formula is essential. There has been a question on the convergence of such calculations. In this paper, choosing the XX model as a simple example, we show explicitly that the Euler–Maclaurin formula reproduces the correct low–temperature expansion of the free energy. ©1997 The Physical Society of Japan

KEYWORDS: finite temperature Baxter formula, Euler–Maclaurin formula, low–temperature expansions, finite size corrections, Heisenberg model, 6–vertex model
URL: http://jpsj.ipap.jp/link?JPSJ/66/988/
DOI: 10.1143/JPSJ.66.988

References | Citing Articles (2)

1. M. Wadati and Y. Akutsu: Prog. Theor. Phys. Suppl. 94 (1988) 1[IPAP].
2. J. Suzuki, Y. Akutsu and M. Wadati: J. Phys. Soc. Jpn. 59 (1990) 2667[IPAP].
3. J. Suzuki, T. Nagao and M. Wadati: Int. J. Mod. Phys. B 6 (1992) 1119.
4. H. Mizuta, T. Nagao and M. Wadati: J. Phys. Soc. Jpn. 63 (1994) 3951[IPAP].
5. K. Nomura: Phys. Rev. B 48 (1993) 16814[APS].
6. A. Kluemper: Z. Phys. B 91 (1993) 507[CrossRef].
7. R. J. Baxter: Exactly Solved Models in Statistical Mechanics (Academic Press, New York, 1982).
8. M. Inoue and M. Suzuki: Prog. Theor. Phys. 78 (1987) 787[IPAP]; ibid. 79 (1988) 645.
9. S. Katsura: Phys. Rev. 127 (1962) 1508[APS].