Journal Menu

- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents

Advances in Mathematical Physics

Volume 2011 (2011), Article ID 808276, 14 pages

http://dx.doi.org/10.1155/2011/808276

Research Article

## A Direct Method for the Analyticity of the Pressure for Certain Classical Unbounded Models

King Fahd University of Petroleum and Minerals, P.O. Box 419, Dhahran 31261, Saudi Arabia

Received 24 November 2010; Accepted 20 January 2011

Academic Editor: Giorgio Kaniadakis

Copyright © 2011 Assane Lo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Linked References

- A. Lo, “On the exponential decay of the $n$-point correlation functions and the analyticity of the pressure,”
*Journal of Mathematical Physics*, vol. 48, no. 12, Article ID 123506, 21 pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet - T. Asano, “Theorems on the partition functions of the Heisenberg ferromagnets,”
*Journal of the Physical Society of Japan*, vol. 29, pp. 350–359, 1970. View at Google Scholar - M. Duneau, D. Iagolnitzer, and B. Souillard, “Decrease properties of truncated correlation functions and analyticity properties for classical lattices and continuous systems,”
*Communications in Mathematical Physics*, vol. 31, pp. 191–208, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - M. Duneau, D. Iagolnitzer, and B. Souillard, “Strong cluster properties for classical systems with finite range interaction,”
*Communications in Mathematical Physics*, vol. 35, pp. 307–320, 1974. View at Publisher · View at Google Scholar - F. Dunlop, “Zeros of the partition function and Gaussian inequalities for the plane rotator model,”
*Journal of Statistical Physics*, vol. 21, no. 5, pp. 561–572, 1979. View at Publisher · View at Google Scholar - J. Glimm and A. Jaffe, “Expansions in statistical physics,”
*Communications on Pure and Applied Mathematics*, vol. 38, no. 5, pp. 613–630, 1985. View at Publisher · View at Google Scholar · View at MathSciNet - J. Glimm and A. Jaffe,
*Quantum Physics. A Functional Integral Point of View*, Springer, New York, NY, USA, 1981. - R. B. Griffiths, “Rigorous results for Ising ferromagnets of arbitrary spin,”
*Journal of Mathematical Physics*, vol. 10, pp. 1559–1565, 1969. View at Publisher · View at Google Scholar - C. Gruber, A. Hintermann, and D. Merlini, “Analyticity and uniqueness of the invariant equilibrium states for general spin $1/2$ classical lattice systems,”
*Communications in Mathematical Physics*, vol. 40, pp. 83–95, 1975. View at Publisher · View at Google Scholar - H. Kunz, “Analyticity and clustering properties of unbounded spin systems,”
*Communications in Mathematical Physics*, vol. 59, no. 1, pp. 53–69, 1978. View at Publisher · View at Google Scholar - J. L. Lebowitz, “Bounds on the correlations and analyticity properties of ferromagnetic Ising spin systems,”
*Communications in Mathematical Physics*, vol. 28, pp. 313–321, 1972. View at Publisher · View at Google Scholar - J. L. Lebowitz, “Uniqueness, analyticity and decay properties of correlations in equilibrium systems,” in
*International Symposium on Mathematical Problems in Theoretical Physics (Kyoto Univ., Kyoto, 1975)*, H. Araki, Ed., Lecture Notes in Phys., 39, pp. 370–379, Springer, Berlin, Germany, 1975. View at Google Scholar - V. A. Malyshev and R. A. Minlos,
*Gibbs Random Fields: The method of cluster expansions*, Nauka, Moscow, Russia, 1985. - C. M. Newman, “Zeros of the partition function for generalized Ising systems,”
*Communications on Pure and Applied Mathematics*, vol. 27, pp. 143–159, 1974. View at Publisher · View at Google Scholar - C. Prakash, “High-temperature differentiability of lattice Gibbs states by Dobrushin uniqueness techniques,”
*Journal of Statistical Physics*, vol. 31, no. 1, pp. 169–228, 1983. View at Publisher · View at Google Scholar - D. Ruelle, “Extension of the Lee-Yang circle theorem,”
*Physical Review Letters*, vol. 26, pp. 303–304, 1971. View at Publisher · View at Google Scholar - D. Ruelle, “Some remarks on the location of zeroes of the partition function for lattice systems,”
*Communications in Mathematical Physics*, vol. 31, pp. 265–277, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - J. Slawny, “Analyticity and uniqueness for spin $1/2$ classical ferromagnetic lattice systems at low temperatures,”
*Communications in Mathematical Physics*, vol. 34, pp. 271–296, 1973. View at Publisher · View at Google Scholar - C. N. Yang and T. D. Lee, “Statistical theory of equations of state and phase transitions. I. Theory of condensation,”
*Physical Review*, vol. 87, pp. 404–409, 1952. View at Google Scholar · View at Zentralblatt MATH - H. J. Brascamp and E. H. Lieb, “On extensions of the Brunn-Minkowski and Prékopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation,”
*Journal of Functional Analysis*, vol. 22, no. 4, pp. 366–389, 1976. View at Google Scholar · View at Zentralblatt MATH - J. Bricmont, J. L. Lebowitz, and C. E. Pfister, “Low temperature expansion for continuous-spin Ising models,”
*Communications in Mathematical Physics*, vol. 78, no. 1, pp. 117–135, 1980/81. View at Publisher · View at Google Scholar - D. C. Brydges and T. Kennedy, “Mayer expansions and the Hamilton-Jacobi equation,”
*Journal of Statistical Physics*, vol. 48, no. 1-2, pp. 19–49, 1987. View at Publisher · View at Google Scholar · View at MathSciNet - R. L. Dobrushin, “Induction on volume and no cluster expansion,” in
*VIIIth International Congress on Mathematical Physics (Marseille, 1986)*, M. Mebkhout and R. Seneor, Eds., pp. 73–91, World Sci. Publishing, Singapore, 1987. View at Google Scholar - R. L. Dobrushin and S. B. Shlosman, “Completely analytical Gibbs fields,” in
*Statistical Physics and Dynamical Systems (Köszeg, 1984)*, J. Fritz, A. Jaffe, and D. Szász, Eds., vol. 10 of*Progr. Phys.*, pp. 371–403, Birkhäuser, Boston, Mass, USA, 1985. View at Google Scholar · View at Zentralblatt MATH - R. L. Dobrushin and S. B. Shlosman, “Completely analytical Gibbs fields,” in
*Statistical Physics and Dynamical Systems (Köszeg, 1984)*, J. Fritz, A. Jaffe, and D. Szász, Eds., vol. 10 of*Progr. Phys.*, pp. 371–403, Birkhäuser, Boston, Mass, USA, 1985. View at Google Scholar · View at Zentralblatt MATH - M. Duneau, B. Souillard, and D. Iagolnitzer, “Decay of correlations for infinite-range interactions,”
*Journal of Mathematical Physics*, vol. 16, pp. 1662–1666, 1975. View at Publisher · View at Google Scholar - F. Dunlop, “Analyticity of the pressure for Heisenberg and plane rotator models,”
*Communications in Mathematical Physics*, vol. 69, no. 1, pp. 81–88, 1979. View at Publisher · View at Google Scholar - O. J. Heilmann, “Zeros of the grand partition function for a lattice gas,”
*Journal of Mathematical Physics*, vol. 11, pp. 2701–2703, 1970. View at Publisher · View at Google Scholar - B. Helffer and J. Sjöstrand, “On the correlation for Kac-like models in the convex case,”
*Journal of Statistical Physics*, vol. 74, no. 1-2, pp. 349–409, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - J. Johnsen, “On the spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb's inequality,”
*Integral Equations and Operator Theory*, vol. 36, no. 3, pp. 288–324, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - K. Gawedski and A. Kupiainen, “Block spin renormalization group for dipole gas and ${(\nabla \phi )}^{4}$,”
*Annals of Physics*, vol. 147, no. 1, pp. 198–243, 1983. View at Publisher · View at Google Scholar - M. Kac,
*Mathematical Mechanism of Phase Transitions*, Gordon & Breach, New York, NY, USA, 1966. - R. Kotecký and D. Preiss, “Cluster expansion for abstract polymer models,”
*Communications in Mathematical Physics*, vol. 103, no. 3, pp. 491–498, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH - E. H. Lieb and A. D. Sokal, “A general Lee-Yang theorem for one-component and multicomponent ferromagnets,”
*Communications in Mathematical Physics*, vol. 80, no. 2, pp. 153–179, 1981. View at Publisher · View at Google Scholar - V. A. Malyaev, “Cluster expansions in lattice models of statistical physics and quantum field theory,”
*Russian Math Surveys*, vol. 35, no. 2, pp. 3–53, 1980. View at Google Scholar - E. Witten, “Supersymmetry and Morse theory,”
*Journal of Differential Geometry*, vol. 17, no. 4, pp. 661–692, 1982. View at Google Scholar · View at Zentralblatt MATH - J. Sjöstrand, “Correlation asymptotics and Witten Laplacians,”
*Algebra and Analysis*, vol. 8, no. 1, pp. 160–191, 1996. View at Google Scholar · View at Zentralblatt MATH - A. Lo, “Witten Laplacian method for the decay of correlations,”
*Journal of Statistical Physics*, vol. 132, no. 2, pp. 355–396, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH