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Conclusions

We have made an accurate characterization of a tricritical point from a series expansion. The minimal exact approximant, and 18 of the other 20 approximants converged with many significant figures to the exact results. The other two had errors mostly of a few percent. The addition of noise enabled us to explore the nature of the convergence under more realistic conditions. We found pleasing convergence to the exact results, even for noise levels far larger than would be found in series calculated with typical precision. We intend to apply the method to various other series [2,3] describing tricritical points in the near future.

Acknowledgments: We thank US-Israel Binational Science Foundation for support of visits of M. E. Fisher to the Technion and of J. Adler to Maryland, during the early stages of this project. We thank the Germany-Israel Foundation (GIF) for support during the later stages, and D. Stauffer for a critical reading of the manuscript. Discussions and correspondence about PDAs and the Anisotropic Heisenberg series with M. E. Fisher, D. Styer, and D. Jasnow, were essential for our reconstruction of the bicritical PDA analysis.


             \begin{references}\bibitem{1}
J. Adler and V. Privman,
J. Phys. A: Math. Gen. {...
...D. Jasnow, and M. E. Fisher,
Phys. Rev. B{\bf 10}, 2088 (1974).
\end{references}


next up previous
Next: About this document ... Up: Series Analysis of Tricritical Previous: Numerical Analysis

1998-12-30