Abstract
Polymer expansion is a useful tool in statistical mechanics and Euclidean field theory. Various examples of polymer systems including high and low temperature expansions of the Ising model, N-component field theory and lattice gauge field theory are presented. We discuss the concepts of Kirkwood-Salsburg equations, Moebius transform, cluster expansion formula of the free energy and thermodynamic limit.
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Abdesselam, A., Rivasseau, V. (1994): Trees, Forests and Jungles: A Botanical Garden for Cluster Expansions, in: Constructive Physics, Proceedings of the Conference held at Ecole Polytechnique, Palaiseau, France 25–27 July 1994, Rivasseau, V. (Ed.), Lecture Notes in Physics, Springer
Brascamp, H. J. (1975): The Kirkwood-Salsburg Equations: Solutions and Spectral Properties, Commun. Math. Phys. 40, 235
Brydges, D. (1984): A Short Course on Cluster Expansions, In Critical Phenomena, Random Systems, Gauge Theories 1984
Cammarota, C. (1982): Decay of Correlations for Infinite Range Interactions in Unbounded Spin Systems, Commun. Math. Phys. 85, 517
Fernando, R., Fröhlich, J., Sokal, A. D. (1992): Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory, Springer
Gallavotti, G., Miracle-Sole, S. (1968): Correlation Functions of a Lattice System, Commun. Math. Phys. 7, 274
Glimm, J., Jaffe, A. (1987): Quantum Physics, Second Edition, Springer
Groeneveld, J. (1962): Two Theorems on Classical Many-Particle Systems, Phys. Lett. Vol. 3, Nr. 1, 50
Gruber, C., Kunz, H. (1971): General Properties of Polymer Systems, Commun. Math. Phys. 22, 133
Heilmann, O. J., Lieb, E. (1970): Monomers and Dimers, Phys. Rev. Lett. 24, Nr. 25, 1412
Itzykson C., Drouffe, J.-M. (1989): Statistical Filed Theory, Volume I and II, Cambridge University Press
Kotecký, R., Preiss, D. (1986): Cluster Expansion for abstract Polymer Models, Commun. Math. Phys. 103, 491
Mack, G., Meyer, H. (1982): A Disorder Parameter that Tests for Confinement in Gauge Theories with Quark Fields, Nucl. Phys. B200[FS4], 249
Mack, G., Pordt, A. (1985): Convergent Perturbation Expansions for Euclidean Quantum Field Theory, Commun. Math. Phys. 97, 267
Mack, G., Pordt, A. (1989): Convergent Weak Coupling Expansions for Lattice Field Theories that Look Like Perturbation Series, Rev. Math. Phys. 1, 47
Pordt, A. (1990): Convergent Multigrid Polymer Expansions and Renormalization for Euclidean Field Theory, DESY 90-020
Pordt, A. (1994): On the Renormalization Group Flows and Polymer Algebras, in: Constructive Physics, Proceedings of the Conference held at Ecole Polytechnique, Palaiseau, France 25–27 July 1994, Rivasseau, V. (Ed.), Lecture Notes in Physics, Springer
Pordt, A. (1996): A Convergence Proof for Linked Cluster Expansions, Uni. Münster preprint MS-TPI-96-05, and e-print archive: hep-lat@xxx.lanl.gov 9604010
Pordt, A. and Reisz, T. (1997): Linked Cluster Expansions Beyond Nearest Neighbour Interactions: Convergence and Graph Classes, Int. Journ. of Mod. Phys. A, Vol. 12, No. 21, 3739
Ruelle, D. (1969): Statistical Mechanics, W. A. Benjamin Inc.
Seiler, E. (1982): Gauge Theories as Problem of Constructive Quantum Field Theory and Statistical Mechanics, Lecture Notes in Physics, Vol. 159, Berlin, Heidelberg, New York, Springer
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Pordt, A. (1998). Polymer expansion in particle physics. In: Meyer-Ortmanns, H., Klümper, A. (eds) Field Theoretical Tools for Polymer and Particle Physics. Lecture Notes in Physics, vol 508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106876
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DOI: https://doi.org/10.1007/BFb0106876
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