Berezinskiǐ-Kosterlitz-Thouless order in two-dimensional O(2)-ferrofluid

Journal of Statistical Physics

Volumn 106, Issue 5-6, 2002, Pages 875-893

  Gruber, Christian ^a   Tamura, Hiroshi ^b   Zagrebnov, Valentin A ^c  

^a EPFL   (Switzerland)

^b KANAZAWA UNIVERSITY   (Japan)

^c CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

Berezinski Kosterlitz Thouless transition; Continuous systems; Ferrofluids; Plane rotators

Indexed keywords

EID: 0036117199     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014021400408     Document Type: Article

References (28)

1. S. Romano and V. A. Zagrebnov, Orientational ordering transition in a continuous-spin ferrofluid, Physica A 253:483-497 (1998).
2. H.-O. Georgii and V. A. Zagrebnov, On the interplay of magnetic and molecular forces in Curie-Weiss ferrofluid models, J. Statist. Phys. 93:79-107 (1998).
3. H.-O. Georgii, O. Häggström, and C. Maes, The random geometry of equilibrium phases, in Phase Transitions and Critical Phenomena, Vol. 18, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 2000).
4. C. Gruber and R. B. Griffiths, Phase transition in a ferromagnetic fluid, Physica A 138:220-230 (1986).
5. B. Widom and J. S. Rowlinson, New model for the study of liquid-vapor phase transition, J. Chem. Phys. 52:1670-1684 (1970).
6. D. Ruelle, Existence of a phase transition in a continuous classical system, Phys. Rev. Lett. 27:1040-1041 (1971).
7. J. L. Lebowitz and E. H. Lieb, Phase transition in a continuum classical system with finite interactions, Phys. Lett. 39A:98-100 (1972).
8. J. Bricmont, K. Kuroda, and J. L. Lebowitz, The structure of Gibbs states and coexistence for non-symmetric continuum Widom-Rowlinson models, Z. Wahrscheinlichkeitstheorie Verw. Geb. 67:121-138 (1984).
9. D. Wells, Ph.D. thesis (Indiana University, 1977).
10. J. Bricmont, J. L. Lebowitz, and Ch.-E. Pfister, Periodic Gibbs states of ferromagnetic spin systems, J. Statist. Phys. 24:269-277 (1981).
11. Ch.-E. Pfister, On the symmetry of the Gibbs states in two-dimensional lattice systems, Commun. Math. Phys. 79: 181-188 (1981).
12. S. B. Shlosman, Continuous models with continuous symmetries in two dimensions, in Random Fields, Vol. 2, J. Fritz, J. L. Lebowitz, and D. Szasz, eds. (North-Holland, Amsterdam, 1979), p. 949.
13. H.-O. Georgii, Gibbs Measures and Phase Transitions (de Gruyter, Berlin/New York, 1988).
14. J. Fröhlich and T. Spencer, The Kosterlitz-Thouless transition in two-dimensional abelian systems and the Coulomb gas, Commun. Math. Phys. 81:527-602 (1981).
15. V. L. Berezinskiǐ, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. Classical systems, Soviet Phys. JETP 32:493-500 (1971).
16. J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6:1181-1203 (1973).
17. M. Campbell and L. Chayes, Intermediate phases in mixed nematic/Heisenberg spin models, J. Phys. A 32:8881-8887 (1999).
18. L. Chayes, S. B. Shlosman, and V. A. Zagrebnov, Discontinuity of the magnetization in diluted O(n)-models, J. Statist. Phys. 98:537-549 (2000).
19. H.-O. Georgii and V. A. Zagrebnov, Entropy-driven phase transitions in multitype lattice gas models, J. Statist. Phys. 102:35-67 (1998).
20. V.A. Zagrebnov, Long-range order in a lattice-gas model of nematic liquid cristals, Physica A 232:737-746 (1996).
21. J. L. Lebowitz, A. E. Mazel, and E. Presutti, Liquid-vapor phase transition for systems with finite range interactions, J. Statist. Phys. 94:955-1025 (1999).
22. J. Ginibre, General formulation of Griffiths' inequalities, Commun. Math. Phys. 16:310-328 (1970).
23. J. L. Lebowitz, GHS and other inequalities, Commun. Math. Phys. 35:87-92 (1974).
24. C. M. Fortuin, P. W. Kasteleyn, and J. Ginibre, Correlation inequalities on some partially ordered sets, Commun. Math. Phys. 22:89-103 (1971).
25. J. Fröhlich, The pure phases (harmonic functions) of generalized processes or: Mathematical physics of phase transitions and symmetry breaking, Bull. Amer. Math. Soc. 84:165-193 (1978).
26. J. Fröhlich, R. Israel, E. H. Lieb, and B. Simon, Phase transitions and reflection positivity I, Commun. Math. Phys. 62:1-34 (1978).
27. J. Bricmont, J. L. Lebowitz, and Ch.-E. Pfister, Some inequalities for anisotropic rotators, in The Wonderful World of Stochastics. A Tribute to Elliott W. Montroll, M. F. Shlesinger and G. H. Weiss, eds. (Elsevier Science Publishers B.V., Amsterdam, 1985), pp. 207-213.
28. F. Dunlop, Correlation inequalities and Kosterlitz-Thouless transition for anisotropic rotators, J. Statist. Phys. 41:733-743 (2000).