A symbolic algorithm for finding exactly soluble statistical mechanical models
- 6 Downloads
In general it is a very difficult task to find statistical mechanical models which satisfy the Yang-Baxter equations and thus are completely integrable. We propose a new approach leading to a (overdetermined) set oflinear equations. The formalism is applied to the Ising and the Ashkin-Teller models, which are both self-duals in two dimensions. Preliminary results for a symbolic algebra manipulation program is given, which would derive the relevant set of equations for an arbitrary internal spin symmetry group.
KeywordsIsing Model Transfer Matrix Matching Condition Statistical Mechanical Model Symbolic Algorithm
Unable to display preview. Download preview PDF.
- 1.For an example see G. Györgyi and P. Ruján, J. Phys., C17, 4207, 1984 and references therein.Google Scholar
- 2.For example the exact solution of the hard hexagon model (R. J. Baxter, J. Phys., A13, L61, 1980, and J. Stat. Phys.,26, 427, 1981) confirmed earlier conjectures regarding the critical exponents of the 3-state Potts model by M. P. M. den Nijs, J. Phys., A12, 1857, 1979.Google Scholar
- 5.P. Ruján, in Lecture Notes in Physics,226, p. 286, ed. N. Sanchez, Springer, New York, 1985.Google Scholar
- 6.R. J. Baxter, Exactly Soved Models in Statistical Mechanics, Academic, London, 1982; P. W. Kasteleyn, in Fundamental Problems in Statistical Mechanics, Vol. 3, p. 103, ed. E. D. G. Cohen, North-Holland, Amsterdam, 1975.Google Scholar
- 7.L. D. Faddeev, Sov. Sci. Rev. Section C (Math. Phys.), Vol.1, ed. P. Novikov, 1981; L. A. Takhtadzhand and L. D. Faddeev, Russian Math. Surveys,34, 11, 1979.Google Scholar
- 26.G. V. Gehlen and V. Rittenberg, to be published.Google Scholar
- 32.“Reduce User’s Manual” by A. C. Hearn, Version 3.1, Rand Publications, 1984 and Seven Reduce Interactive Lessons, by D. R. Stoutmayer.Google Scholar