Abstract
The grand-partition-function-zero method is applied to lattice systems of rigid molecules, based on the algebraic technique of Ruelle. Consideration of small collections of lattice molecules, through this approach, provides rigorous delineation of regions of the complex activity plane which are free of zeros of the grand partition function, and hence free of thermodynamic singularities. Two conjectures, as yet unproved, are offered, which greatly reduce the computational effort required in using the technique. A simple proof is provided for the absence of physical phase transitions in monomerdimer systems, and bounds are obtained on the locations of the transitions of other lattice gases.
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References
C. N. Yang and T. D. Lee,Phys. Rev. 87:404, 410 (1952).
T. Asano,J. Phys. Soc. Japan 29:350 (1970);Phys. Rev. Letters 24:1409 (1970).
M. Suzuki and M. E. Fisher,J. Math. Phys. 12:235 (1971).
D. Ruelle,Phys. Rev. Letters 26:303 (1971).
G. Gallavotti, S. Miracle-Sole, and D. W. Robinson,Phys. Letters 25A:493 (1967).
L. Onsager,Phys. Rev. 65:404 (1952).
E. Meeron,Phys. Rev. Letters 25:152 (1970).
L. K. Runnels and L. L. Combs,J. Chem. Phys. 45:2482 (1966); D. S. Gaunt and M. E. Fisher,J. Chem. Phys. 43:2840 (1965).
D. S. Gaunt,J. Chem. Phys. 46:3237 (1967).
L. K. Runnels,J. Math. Phys. 11:842 (1970).
O. J. Heilmann and E. H. Lieb,Phys. Rev. Letters 24:1412 (1970).
O. J. Heilmann, private communication.
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Research supported in part by National Science Foundation Grant GP-17026.
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Runnels, L.K., Hubbard, J.B. Applications of the Yang-Lee-Ruelle theory to hard-core lattice gases. J Stat Phys 6, 1–20 (1972). https://doi.org/10.1007/BF01060198
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DOI: https://doi.org/10.1007/BF01060198