Ferroelectric and dipolar glass phases of noncrystalline systems

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 56, Issue 1 SUPPL. B, 1997, Pages 562-570

  Ayton, G ^a   Gingras, M J P ^b,c   Patey, G N ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b TRIUMF   (Canada)

^c UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000984874     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.56.562     Document Type: Article

References (47)

1. D. Wei and G. N. Patey, Phys. Rev. Lett. 68, 2043 (1992) Phys. Rev. A 46, 7783 (1992).
2. D. Wei and G. N. Patey, Phys. Rev. Lett. 68, 2043 (1992) Phys. Rev. A 46, 7783 (1992).
3. J. J. Weis, D. Levesque, and G. J. Zarragoicoechea, Phys. Rev. Lett. 69, 913 (1992).
4. R. Tao and J. M. Sun, Phys. Rev. Lett. 67, 398 (1991).
5. One actually expects that the bond order parameter describing the orientation of the nearest-neighbor lattice bonds of the short-range tetragonal-I structure is driven long-range order at the ferroelectric transition similar to what happens to the induced long-range hexatic ordering at the smectic-A to smectic-C transition in liquid crystals [see M. J. P. Gingras and P. C. W. Holdsworth, Phys. Rev. Lett. 74, 202 (1995)].
6. U. T. Höchli and M. Maglione, J. Phys., Condens. Matter 1, 2241 (1989); U. T. Höchl, K. Knorr, and A. Loidl, Adv. Phys. 39, 405 (1990).
7. U. T. Höchli and M. Maglione, J. Phys., Condens. Matter 1, 2241 (1989); U. T. Höchl, K. Knorr, and A. Loidl, Adv. Phys. 39, 405 (1990).
8. W. Luo, S. R. Nagel, T. F. Rosenbaum, and R. E. Rosenweig, Phys. Rev. Lett. 67, 2721 (1991); T. Jonsson, J. Mattsson, C. Djurberg, F. A. Khan, P. Nordblad, and P. Svedlindh, Phys. Rev. Lett. 75, 4138 (1995).
9. W. Luo, S. R. Nagel, T. F. Rosenbaum, and R. E. Rosenweig, Phys. Rev. Lett. 67, 2721 (1991); T. Jonsson, J. Mattsson, C. Djurberg, F. A. Khan, P. Nordblad, and P. Svedlindh, Phys. Rev. Lett. 75, 4138 (1995).
10. B. E. Vugmeister and M. D. Glinchuk, Rev. Mod. Phys. 62, 4 (1990).
11. K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986); K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, 1991).
12. K. Binder and A. P. Young, Rev. Mod. Phys. 58, 801 (1986); K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, 1991).
13. 4 moment. The effect of this transition on the magnetic properties of the frozen ferrofluid remains to be explored.
14. Random anisotropy added to vector spin glasses with short-range random exchange interactions is believed to display ordering at nonzero temperature in the universality class of the short-range Ising spin glass model [see Ref. [8] and M. J. P. Gingras, Phys. Rev. Lett. 71, 1637 (1993)]. Quite possibly, dipolar glass ordering is also at nonzero temperature and in the short-range Ising spin glass universality class [see A. J. Bray, M. A. Moore, and A. P. Young, Phys. Rev. Lett. 56, 2641 (1986)].
15. Random anisotropy added to vector spin glasses with short-range random exchange interactions is believed to display ordering at nonzero temperature in the universality class of the short-range Ising spin glass model [see Ref. [8] and M. J. P. Gingras, Phys. Rev. Lett. 71, 1637 (1993)]. Quite possibly, dipolar glass ordering is also at nonzero temperature and in the short-range Ising spin glass universality class [see A. J. Bray, M. A. Moore, and A. P. Young, Phys. Rev. Lett. 56, 2641 (1986)].
16. For compactness, we shall refer here only to ferroelectric order, but the discussion and results apply to ferromagnetic order of dipolar origin as well.
17. Glasslike ground states are a generic feature of randomly disordered molecular systems, and the overall behavior applies not only to the dipolar case. It can also happen for intermolecular potentials where there is an explicit intermolecular vector coupling to molecular orientation, and where mean-field theory assuming annealed translation degrees of freedom, might predict long-range liquid-crystalline order. In a liquid phase, local short-range correlation can be "self-thermally" tuned to allow for a liquid-crystalline phase, while the same intermolecular potential in systems with quenched random positional disorder will develop orientational molecular glass order [see for example, P. C. W. Holdsworth et al., J. Phys., Condens. Matter 3, 6679 (1991); M. J. P. Gingras et al., Mol. Cryst. Liq. Cryst. 204, 177 (1991); P. C. W. Holdsworth et al., in Disorder in Condensed Matter Physics, edited by J. A. Blackman and J. Tagüeña (Oxford University Press, Oxford, 1991)]. The glasslike ground state arises from the infrared divergence of random frozen deviations "transverse" to the uniform order in quenched systems via an Imry-Ma-type instability [see Y. Imry and S.-K. Ma, Phys. Rev. Lett. 35, 1399 (1975); and principally A. Aharony, Solid State Commun. 28, 667 (1978)]. This destroys longitudinal long-range order and, subsequently, leads to a renormalization-group flow at large length scale toward an anisotropic multipolar glass fixed point. However, unlike short-range intermolecular potentials, dipolar interactions are long ranged, and the role of the reaction field (which arises from the surrounding continuum) in stabilizing ferroelectric order by cutting off the infrared divergence for n-component (n>1) dipoles remains to be sorted out.
18. Glasslike ground states are a generic feature of randomly disordered molecular systems, and the overall behavior applies not only to the dipolar case. It can also happen for intermolecular potentials where there is an explicit intermolecular vector coupling to molecular orientation, and where mean-field theory assuming annealed translation degrees of freedom, might predict long-range liquid-crystalline order. In a liquid phase, local short-range correlation can be "self-thermally" tuned to allow for a liquid-crystalline phase, while the same intermolecular potential in systems with quenched random positional disorder will develop orientational molecular glass order [see for example, P. C. W. Holdsworth et al., J. Phys., Condens. Matter 3, 6679 (1991); M. J. P. Gingras et al., Mol. Cryst. Liq. Cryst. 204, 177 (1991); P. C. W. Holdsworth et al., in Disorder in Condensed Matter Physics, edited by J. A. Blackman and J. Tagüeña (Oxford University Press, Oxford, 1991)]. The glasslike ground state arises from the infrared divergence of random frozen deviations "transverse" to the uniform order in quenched systems via an Imry-Ma-type instability [see Y. Imry and S.-K. Ma, Phys. Rev. Lett. 35, 1399 (1975); and principally A. Aharony, Solid State Commun. 28, 667 (1978)]. This destroys longitudinal long-range order and, subsequently, leads to a renormalization-group flow at large length scale toward an anisotropic multipolar glass fixed point. However, unlike short-range intermolecular potentials, dipolar interactions are long ranged, and the role of the reaction field (which arises from the surrounding continuum) in stabilizing ferroelectric order by cutting off the infrared divergence for n-component (n>1) dipoles remains to be sorted out.
19. Glasslike ground states are a generic feature of randomly disordered molecular systems, and the overall behavior applies not only to the dipolar case. It can also happen for intermolecular potentials where there is an explicit intermolecular vector coupling to molecular orientation, and where mean-field theory assuming annealed translation degrees of freedom, might predict long-range liquid-crystalline order. In a liquid phase, local short-range correlation can be "self-thermally" tuned to allow for a liquid-crystalline phase, while the same intermolecular potential in systems with quenched random positional disorder will develop orientational molecular glass order [see for example, P. C. W. Holdsworth et al., J. Phys., Condens. Matter 3, 6679 (1991); M. J. P. Gingras et al., Mol. Cryst. Liq. Cryst. 204, 177 (1991); P. C. W. Holdsworth et al., in Disorder in Condensed Matter Physics, edited by J. A. Blackman and J. Tagüeña (Oxford University Press, Oxford, 1991)]. The glasslike ground state arises from the infrared divergence of random frozen deviations "transverse" to the uniform order in quenched systems via an Imry-Ma-type instability [see Y. Imry and S.-K. Ma, Phys. Rev. Lett. 35, 1399 (1975); and principally A. Aharony, Solid State Commun. 28, 667 (1978)]. This destroys longitudinal long-range order and, subsequently, leads to a renormalization-group flow at large length scale toward an anisotropic multipolar glass fixed point. However, unlike short-range intermolecular potentials, dipolar interactions are long ranged, and the role of the reaction field (which arises from the surrounding continuum) in stabilizing ferroelectric order by cutting off the infrared divergence for n-component (n>1) dipoles remains to be sorted out.
20. Glasslike ground states are a generic feature of randomly disordered molecular systems, and the overall behavior applies not only to the dipolar case. It can also happen for intermolecular potentials where there is an explicit intermolecular vector coupling to molecular orientation, and where mean-field theory assuming annealed translation degrees of freedom, might predict long-range liquid-crystalline order. In a liquid phase, local short-range correlation can be "self-thermally" tuned to allow for a liquid-crystalline phase, while the same intermolecular potential in systems with quenched random positional disorder will develop orientational molecular glass order [see for example, P. C. W. Holdsworth et al., J. Phys., Condens. Matter 3, 6679 (1991); M. J. P. Gingras et al., Mol. Cryst. Liq. Cryst. 204, 177 (1991); P. C. W. Holdsworth et al., in Disorder in Condensed Matter Physics, edited by J. A. Blackman and J. Tagüeña (Oxford University Press, Oxford, 1991)]. The glasslike ground state arises from the infrared divergence of random frozen deviations "transverse" to the uniform order in quenched systems via an Imry-Ma-type instability [see Y. Imry and S.-K. Ma, Phys. Rev. Lett. 35, 1399 (1975); and principally A. Aharony, Solid State Commun. 28, 667 (1978)]. This destroys longitudinal long-range order and, subsequently, leads to a renormalization-group flow at large length scale toward an anisotropic multipolar glass fixed point. However, unlike short-range intermolecular potentials, dipolar interactions are long ranged, and the role of the reaction field (which arises from the surrounding continuum) in stabilizing ferroelectric order by cutting off the infrared divergence for n-component (n>1) dipoles remains to be sorted out.
21. Glasslike ground states are a generic feature of randomly disordered molecular systems, and the overall behavior applies not only to the dipolar case. It can also happen for intermolecular potentials where there is an explicit intermolecular vector coupling to molecular orientation, and where mean-field theory assuming annealed translation degrees of freedom, might predict long-range liquid-crystalline order. In a liquid phase, local short-range correlation can be "self-thermally" tuned to allow for a liquid-crystalline phase, while the same intermolecular potential in systems with quenched random positional disorder will develop orientational molecular glass order [see for example, P. C. W. Holdsworth et al., J. Phys., Condens. Matter 3, 6679 (1991); M. J. P. Gingras et al., Mol. Cryst. Liq. Cryst. 204, 177 (1991); P. C. W. Holdsworth et al., in Disorder in Condensed Matter Physics, edited by J. A. Blackman and J. Tagüeña (Oxford University Press, Oxford, 1991)]. The glasslike ground state arises from the infrared divergence of random frozen deviations "transverse" to the uniform order in quenched systems via an Imry-Ma-type instability [see Y. Imry and S.-K. Ma, Phys. Rev. Lett. 35, 1399 (1975); and principally A. Aharony, Solid State Commun. 28, 667 (1978)]. This destroys longitudinal long-range order and, subsequently, leads to a renormalization-group flow at large length scale toward an anisotropic multipolar glass fixed point. However, unlike short-range intermolecular potentials, dipolar interactions are long ranged, and the role of the reaction field (which arises from the surrounding continuum) in stabilizing ferroelectric order by cutting off the infrared divergence for n-component (n>1) dipoles remains to be sorted out.
22. H.-J. Xu, Ph.D. thesis, University of British Columbia, 1992.
23. H. Zhang and M. Widom, J. Magn. Magn. Mater. 122, 119 (1993).
24. H. Zhang and M. Widom, Phys. Rev. B 51, 8951 (1995).
25. G. Ayton, M. J. P. Gingras, and G. N. Patey, Phys. Rev. Lett. 75, 2360 (1995).
26. M. J. P. Gingras, in Magnetic Systems with Competing Interactions, edited by H. T. Diep (World Scientific, Singapore, 1994), p. 238.
27. H.-J. Xu, B. Bergersen, and Z. Racz, J. Phys. Condens. Matter 4, 2035 (1992).
28. N. Kawashima and A. P. Young, Phys. Rev. B 53, R484 (1996).
29. R. Pirc, B. Tadic, and R. Blinc, Z. Phys. B 61, 69 (1985); Phys. Rev. B 36, 8607 (1987); B. Tadic, R. Pirc, and R. Blinc, Z. Phys. B 75, 249 (1989).
30. R. Pirc, B. Tadic, and R. Blinc, Z. Phys. B 61, 69 (1985); Phys. Rev. B 36, 8607 (1987); B. Tadic, R. Pirc, and R. Blinc, Z. Phys. B 75, 249 (1989).
31. R. Pirc, B. Tadic, and R. Blinc, Z. Phys. B 61, 69 (1985); Phys. Rev. B 36, 8607 (1987); B. Tadic, R. Pirc, and R. Blinc, Z. Phys. B 75, 249 (1989).
32. S. W. de Leeuw, J. W. Perram, and E. R. Smith, Annu. Rev. Phys. Chem. 37, 245 (1986); Proc. R. Soc. London Ser. A 373, 27 (1980); 388, 177 (1983).
33. S. W. de Leeuw, J. W. Perram, and E. R. Smith, Annu. Rev. Phys. Chem. 37, 245 (1986); Proc. R. Soc. London Ser. A 373, 27 (1980); 388, 177 (1983).
34. S. W. de Leeuw, J. W. Perram, and E. R. Smith, Annu. Rev. Phys. Chem. 37, 245 (1986); Proc. R. Soc. London Ser. A 373, 27 (1980); 388, 177 (1983).
35. P. G. Kusalik, J. Chem. Phys. 93, 3520 (1990).
36. J. R. Thompson, Hong Guo, D. H. Ryan, M. J. Zuckerman, and Martin Grant, Phys. Rev. B 45, 3129 (1992).
37. The critical volume fractions are 0.157 for the Ising system and 0.295 for the XYZ model [14,15]. Using the effective hard sphere diameter 0.967σ [see J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, 2nd ed. (Academic, London, 1986), Chap. 6] the soft-sphere densities p* = 0.8 and 1.05 correspond to volume fractions of 0.379 and 0.497, respectively.
38. M. P. Allen and D. J. Tildesely, Computer Simulation of Liquids (Clarendon, Oxford, 1989).
39. B. Bergersen and Z. Rácz, Phys. Rev. Lett. 67, 3047 (1991); H.-J. Xu, B. Bergersen, and Z. Rácz, Phys. Rev. E 47, 1520 (1993).
40. B. Bergersen and Z. Rácz, Phys. Rev. Lett. 67, 3047 (1991); H.-J. Xu, B. Bergersen, and Z. Rácz, Phys. Rev. E 47, 1520 (1993).
41. We note that other decoupled simulation schemes could be used for the Ising model. For example, if 100 MD time steps are performed between MC sweeps, mass dependence is observed, with the transition moving to higher temperatures for lighter masses. However, in the large mass limit one again recovers the results shown in Fig. 7.
42. Here, as in Levy flight systems [26], we are dealing with non-equilibrium conditions. Therefore, the heat capacity obtained from the temperature derivative of the energy need not and does not agree with that estimated from energy fluctuations.
43. C. J. F. Böttcher, Theory of Electric Polarization, 2nd ed. (Elsevier, Amsterdam, 1973).
44. H. Fröhlich, Theory of Dielectrics, 2nd ed. (Oxford University Press, Oxford, 1958).
45. H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed. (Wiley, New York, 1985); B. Bergersen and M. Plischke, Equilibrium Statistical Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1989), Chap. 3.
46. H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed. (Wiley, New York, 1985); B. Bergersen and M. Plischke, Equilibrium Statistical Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1989), Chap. 3.
47. See N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, Reading MA, 1992), and Ref. [8].