N dependence of upper bounds of critical temperatures of 2D O(N) spin models

Communications in Mathematical Physics

Volumn 202, Issue 1, 1999, Pages 127-168

  Ito, K R ^a,c   Tamura, H ^b  

^a SETSUNAN UNIVERSITY   (Japan)

^b KANAZAWA UNIVERSITY   (Japan)

^c KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033244737     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050577     Document Type: Article

References (23)

1. 1. Balaban, T., Brydges, D., Imbrie, J. and Jaffe, A.: The Mass Gap for Higgs Models on a Unit Lattice. Ann. Physics 158, 281 (1984)
2. 2. Brascamps, M. and Lieb, E.: On extensions of the Brunn-Minkowski and Prekopa-Leinder Theorem, including Inequalities for Log Concave Functions with Some Applications. J. Funct. Anal. 22, 336-389 (1976)
3. 3. Brydges, D., Fröhlich, J. and Spencer, T.: The Random Walk Representation of Classical Spin Systems and Correlation Inequalities. Commun. Math. Phys. 83, 123-150 (1982)
4. 4. Brydges, D., Fröhlich, J. and Sokal, A.: The Random Walk Representation of Classical Spin Systems and Correlation Inequalities, II. Commun. Math. Phys. 91, 117-139 (1985)
5. 5. Brydges, D.: A Short Course on Cluster Expansions. In: Les Houches Summer School, Session XLIII (1984), ed. by K. Osterwalder et al. London. Elsevier Sci. Publ., 1986, pp. 129-183
6. 5. Phys. Rev. Letters 75, 1891-1894 (1995)
7. 7. Fröhlich, J., Israel, R., Lieb, E. and Simon, B.: Phase Transitions and Reflection Positivity. I.. Commun. Math. Phys. 62, 1-34 (1978); J. Fröhlich, R. Israel, E. Lieb and B. Simon , Phase Transitions and Reflection Positivity. II.. J. Stat. Phys. 22, 297-347 (1980)
8. 7. Fröhlich, J., Israel, R., Lieb, E. and Simon, B.: Phase Transitions and Reflection Positivity. I.. Commun. Math. Phys. 62, 1-34 (1978); J. Fröhlich, R. Israel, E. Lieb and B. Simon , Phase Transitions and Reflection Positivity. II.. J. Stat. Phys. 22, 297-347 (1980)
9. 4 Theory, Rigorous Control of a Renormalizable Asymptotically Free Model. Commun. Math. Phys. 99, 197-252 (1985)
10. 2 Models and Other Applications, Part II, The cluster expansion. In: Constructive Quantum Field Theory; Lecture Notes in Physics, 25, ed. by G.Velo and A. Wightman, Heidelberg, Springer Verlag, 1973, pp. 199-242
11. 10. Ito, K.R.: Permanent Quark Confinement in 4D Hierarchical Lattice Gauge Models of Migdal-Kadanoff Type. Phys. Rev. Letters 55, 558-561 (1985); Mass Generations in Two-Dimensional Hierarchical Heisenberg Model of Migdal-Kadanoff Type. Commun. Math. Phys. 110, 237-246 (1987); Renormalization Group Flow of Two-Dimensional Hierarchical Heisenberg Model of Dyson-Wilson Type. Commun. Math.Phys. 137, 45-70 (1991)
12. 10. Ito, K.R.: Permanent Quark Confinement in 4D Hierarchical Lattice Gauge Models of Migdal-Kadanoff Type. Phys. Rev. Letters 55, 558-561 (1985); Mass Generations in Two-Dimensional Hierarchical Heisenberg Model of Migdal-Kadanoff Type. Commun. Math. Phys. 110, 237-246 (1987); Renormalization Group Flow of Two-Dimensional Hierarchical Heisenberg Model of Dyson-Wilson Type. Commun. Math.Phys. 137, 45-70 (1991)
13. 10. Ito, K.R.: Permanent Quark Confinement in 4D Hierarchical Lattice Gauge Models of Migdal-Kadanoff Type. Phys. Rev. Letters 55, 558-561 (1985); Mass Generations in Two-Dimensional Hierarchical Heisenberg Model of Migdal-Kadanoff Type. Commun. Math. Phys. 110, 237-246 (1987); Renormalization Group Flow of Two-Dimensional Hierarchical Heisenberg Model of Dyson-Wilson Type. Commun. Math.Phys. 137, 45-70 (1991)
14. 11. Ito, K.R., Kugo, T. and Tamura, H.: Representation of O(N) Spin Models by Self-Avoiding Random Walks. Commun. Math. Phys. 183, 723-736 (1997)
15. 12. Ito, K.R. and Tamura, H.: Deviations of Upper Bounds of Critical Temperatures of 2D O(N) Spin Models. To appear in Letters in Math. Phys. (1998)
16. 13. Kotecky, R. and Preiss, D.: Cluster Expansion for Abstract Polymer Models. Commun. Math. Phys. 103, 491-498 (1986)
17. 14. Kupiainen, A.: On the 1/n expansion. Commun. Math. Phys. 73, 273-294 (1980)
18. 15. Ma, S.K.: The 1/n expansion. In: Phase Transitions and Critical Phenomena, 6, ed. by C. Domb and M. S. Green, London: Academic Press, 1976, pp. 249-292
19. 16. Rivasseau, V.: Cluster Expansion with Small/Large Field Conditions. In: Mathematical Quantum Theory I, Field Theory and Many-Body Theory, ed. by J. Feldman et al., (CRM Proceedings and Lecture Notes, Vol.7, Providence, RI: Am. Math. Soc., 1994
20. 2 Euclidean (Quantum) Field Theory. Princeton Series in Physics, Princeton, N.J.: Princeton Univ. Press, 1974
21. 18. Wilson, K.: Confinement of Quarks, Phys. Rev. D 10, 2445-2459 (1974); Polyakov, A.: Interactions of Goldstone Bosons in Two Dimensions. Phys. Lett. 59B, 79-81 (1975)
22. 18. Wilson, K.: Confinement of Quarks, Phys. Rev. D 10, 2445-2459 (1974); Polyakov, A.: Interactions of Goldstone Bosons in Two Dimensions. Phys. Lett. 59B, 79-81 (1975)
23. 19. Kopper, C.: Mass Generation in the large W-nonlinear σ-Model. Commun. Math. Phys. 202, 89-126 (1999)