Representations of O(N) spin models by self-avoiding random walks

Communications in Mathematical Physics

Volumn 183, Issue 3, 1997, Pages 723-737

  Ito, K R ^a,c   Kugo, T ^b   Tamura, H ^b  

^a SETSUNAN UNIVERSITY   (Japan)

^b KANAZAWA UNIVERSITY   (Japan)

^c KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031066538     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050049     Document Type: Article

References (23)

1. Alm, S. E.: Upper bounds on the connective constant of self-avoiding walks. Combin. Probab. Comput. 2, 115-136 (1993)
2. Baillie, C. F., Gupta, R., Hawick, K. and Pawley, G.: Monte Carlo Renormalization Group Study of the Three Dimensional Ising Model. Phys. Rev. B45, 10438-10453 (1992)
3. Binder, K.: Finite Size Scaling Analysis of Ising Model Block Distribution Functions. Z. Phys. B43, 119-140 (1981)
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. 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)
6. Fisher, M. E.: Critical Temperatures of Anisotropic Ising Lattice. II. General Upper Bounds. Phys. Rev. 162, 480-485 (1967)
7. Gottlob, A. P., Hasenbusch, M.: Critical Behavior of the 3D XY-Model: A Monte Carlo study. Nucl. Phys. Proc. Suppl. B30, 838-841 (1993)
8. Holm, C. and Janke, W.: High Precision Single-Cluster Monte Carlo Measurement of the Critical Exponents of the Classical 3D Heisenberg Model. Nucl. Phys. Proc. Suppl. B30, 846-849 (1993)
9. Ito, K. R.: Random Walk Representations and Mayer Expansion. In: H. Araki et al. (eds.), Quantum and Non-Commutative Analysis., Netherlands: Kluwer Academic Publishers, 1993 p.119
10. Ito, K. R., Kugo, T. and Tamura, H.: Rigorous Bounds for Critical Temperatures of O(N) Spin Models by Transformations of Block Spin Type. Lett. Math. Phys. 37, 349-362 (1996)
11. Ito, K. R., Kugo, T. and Tamura, H.: Accurate Bounds for Critical Temperatures of O(N) Spin models by Renormalized Random Walk Representations. Phys. Lett. A210, 175-182 (1996)
12. Ito, K. R., Kugo, T. and Tamura, H.: Self-Avoiding Walk Representation of Classical Spin Models and Bounds for the Critical Temperatures. Preprint
13. Kanaya, K. and Kaya, S.: Critical Exponent of a Three Dimesional O(4) Spin Model. Tsukuba Univ. Preprint UTHEP-284 (1994, Sept.)
14. 4 Theory. Nucl. Phys. Proc. Suppl. B4, 422-426 (1988)
15. 4 Theory. Nucl. Phys. Proc. Suppl. B4, 422-426 (1988)
16. Lieb, E.: A Refinement of Simon's Correlation Inequality. Commun. Math. Phys. 77, 127-135 (1980)
17. 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,
18. Madras, N. and Slade, G.: The Self-Avoiding Walk. Boston: Birkhäuser, 1993
19. Nemirovsky, A., Freed, K., Ishinabe, T. and Douglas, J.: Marriage of Exact Enumeration and 1/d Expansion Methods: Lattice Model of Dilute Polymers. J. Stat. Phys. 67, 1083-1108 (1992)
20. Polyakov, A. M.: Interactions of Goldstone Particles in Two-Dimensions. Applications to Ferromagnets and Massive Yang-Mills Fields. Phys. Lett. B59, 79-81 (1975); Kogut, J. B.: An Introduction to Lattice Gauge Theory and Spin Systems. Rev. Mod. Phys. 51, 659-713 (1979)
21. Polyakov, A. M.: Interactions of Goldstone Particles in Two-Dimensions. Applications to Ferromagnets and Massive Yang-Mills Fields. Phys. Lett. B59, 79-81 (1975); Kogut, J. B.: An Introduction to Lattice Gauge Theory and Spin Systems. Rev. Mod. Phys. 51, 659-713 (1979)
22. Symanzik, K.: Euclidean Quantum Field Theory. In: Jost, R. (eds.), Local Quantum Theory. New York, London: Academic Press, 1969
23. Wolff, U.: Collective Monte Carlo Updating in a High Precision Study of the x-y Model. Nucl. Phys. B322, 759-774 (1989)