Abstract
A detailed analysis is reported examining the local magnetic susceptibility χ(r), in relation to the correlation functionG(R) and correlation length ζ, of a spherical model ferromagnet confined to geometryΩ =L d −d′ × ∞d′ (d′≤2,d>2) under a continuous set oftwisted boundary conditions. The “twist” parameter\(\underline \tau \) in this problem may be interpreted as a measure of the geometry-dependent doping level of interfacial impurities (or antiferromagnetic seams) in theextended system at various temperatures. For τ j →0, ∀j∈d-d′, no seams are present except at infinity, whereas if τ j = 1/2, impurity saturation occurs. For 0 < τ j < 1/2 the physical domainΩ phys =D d −d′ × ∞d′ (D>L), defining the region between seams containing the origin, depends on temperature above a certain threshold (T>T 0). Below that temperature (T>T 0), seams are frozen at the same position (D≈L/2τ,d-d'=1), revealing a smoothly varying largescale structural phase transition.
Similar content being viewed by others
References
D. Jasnow, inPhase Transitions and Critical Phenomena, Vol. 10, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1986), p. 269.
D. B. Abraham, inPhase Transitions and Critical Phenomena, Vol. 10, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1986), p. 1.
G. Forgacs, R. Lipowsky and Th. M. Nieuwenhuizen, inPhase Transitions and Critical Phenomena, Vol. 14, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1991), p. 135.
K. Binder, inPhase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1983), p. 1.
H. W. Diehl, inPhase Transitions and critical Phenomena, Vol. 10, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1986), p. 75.
D. Nelson, inStatistical Mechanics of Membranes and Surfaces, D. Nelson, T. Piran, and S. Weinberg, eds. (World Scientific, Singapore, 1988), p. 1.
M. E. Fisher, inStatistical Mechanics of Membranes and Surfaces, D. Nelson, T. Piran, and S. Weinberg, eds. (World Scientific, Singapore, 1988), p. 19.
S. Leibler, inStatistical Mechanics of Membranes and Surfaces, D. Nelson, T. Piran, and S. Weinberg eds. (World Scientific, Singapore, 1988), p. 45.
L. V. Mikeev and M. E. Fisher,Phys. Rev. Lett. 70:186 (1993).
V. Privman,Int. J. Mod. Phys. C 3:857 (1992), and references therein.
S. Singh, R. K. Pathria, and M. E. Fisher,Phys. Rev. B 33:6415 (1986).
E. Eisenriegler,Z. Phys. B—Condensed Matter 61:299 (1985).
D. B. Abraham and M. A. Robert,J. Phys. A 12:L129 (1979);J. Phys. A 13:2229 (1980).
A. E. Patrick,J. Stat. Phys. 75:253 (1994);J. Stat. Phys. 72:665 (1993).
A. M. Khorunzhy, B. A. Khoruzhenko, L. A. Pastur, and M. V. Shcherbina inPhase Transitions and Critical Phenomena, Vol. 15, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1992), p. 73.
L. Frachebourg and M. Henkel,Physica A 195:577 (1993).
M. N. Barber and M. E. Fisher,Ann. Phys. (NY)77:1 (1973).
M. Henkel,J. Phys. A 21:L227 (1988); M. Henkel and R. A. Weston,J. Phys. A 25:L207 (1992).
S. Allen and R. K. Pathria,J. Phys. A 26:6797 (1993).
S. Allen and R. K. Pathria,Phys. Rev. B 50:6765 (1994).
S. Allen, Ph.D. thesis, University of Waterloo (1994), Section 1.1.
S. Chakravarty,Phys. Rev. Lett. 66:481 (1991).
E. Brézin, E. Korutcheva, Th. Jolicoeur, and J. Zinn-Justin,J. Stat. Phys. 70:583 (1993).
G. S. Joyce, inPhase Transitions and Critical Phenomena, Vol. 2, C. Domb and M. S. Green, eds. (Academic Press, New York, 1972), p. 375.
I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series and Products A. Jeffrey, ed. (Academic Press, New York, 1980), 6.596#3.
M. E. Fisher and P. J. Upton,Phys. Rev. Lett. 65:3405 (1990).
M. E. Fisher and V. Privman,Phys. Rev. B 32:447 (1985); see also V. Privman, inFinite-Size Scaling and Numerical Simulation of Statistical Systems, V. Privman ed. (World Scientific, Singapore, 1990), p. 1.
S. Singh and R. K. Pathria,Phys. Rev. B 36:3769 (1987).
M. E. Fisher, M. N. Barber, and D. Jasnow,Phys. Rev. A 8:1111 (1973).
S. Allen and R. K. Pathria,J. Math. Phys. 34:1497 (1993).
W. Selke, inPhase Transitions and Critical Phenomena, Vol. 15, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1992), p. 1; see also M. den Nijs, inPhase Transitions and Critical Phenomena, Vol. 12, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1988), p. 219.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Allen, S. Interface formation and a structural phase transition for the spherical model of ferromagnetism. J Stat Phys 79, 165–181 (1995). https://doi.org/10.1007/BF02179385
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02179385