Abstract
We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.
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References
M. Goldhaber, Private communication.
P. G. de Gennes,Physics of Liquid Crystals (Oxford University Press, 1976).
A. B. Pippard,Classical Thermodynamics (Cambridge University Press, 1966).
B. I. Halperin, T. C. Lubensky, and S. K. Ma,Phys. Rev. Lett. 32:292 (1974);
B. I. Halperin and T. C. Lubensky,Solid State Commun. 14:997 (1974).
D. L. Johnson,J. Chim. Phys. 80:45 (1983), L. J. Martinez-Miranda, A. R. Kortan, and R. J. Birgenau,Phys. Rev. A 36:2372 (1987) and references therein; see also M. A. Anisimov,Molecular Crystals Liquid Crystals (1988).
T. C. Lubensky,J. Chem. Phys. 80:6 (1983).
J. Thoen, H. Marynissen, and W. van Dael,Phys. Rev. Lett. 52:204 (1984);
H. Marynissen, J. Thoen, and W. van Dael,Mol. Cryst. Liq. Cryst. 124:195 (1985);
J. Thoen, H. Marynissen, and W. van Dael,Phys. Rev. 26A:2886 (1982).
B. M. Ocko, R. J. Birgeneau, and J. D. Litster,Z. Phys. B 62:487 (1986).
M. A. Anisimov, V. P. Voronov, E. E. Gorodetskii, V. E. Podnek, and F. Kholmudorov,JETP Lett. 45:425 (1987) [Pisma Zh. Eksp. Teor. Fiz. 45:336 (1987)].
P. E. Cladis, W. van Saarloos, D. A. Huse, J. S. Patel, J. W. Goodby, and P. L. Finn,Phys. Rev. Lett. 62:1764 (1989).
A. Anisimov, P. E. Cladis, E. E. Gorodetskii, D. A. Huse, V. E. Podneks, V. G. Taratuta, W. van Saarloos, and V. P. Voronov,Phys. Rev. A 41:6749 (1990).
David L. Goodstein,States of Matter (Prentice-Hall, Englewood Cliffs, New Jersey, 1975).
L. Landau and L. Lifshitz,Statistical Physics (Pergamon, New York, 1980), Vol. 5, p. 258.
P. Pfeuty and G. Toulouse,Introduction to the Renormalization Group and to Critical Phenomena (Wiley, New York, 1977).
P. W. Anderson, inSymmetries and Broken Symmetries in Condensed Matter Physics, N. Boccara, ed. (IDSET, Paris, 1981).
Shang-Keng Ma,Statistical Mechanics (World Scientific, Singapore, 1985).
W. MacMillan,Phys. Rev. A 6:936 (1972).
P. G. de Gennes,Solid Stale Commun. 10:753 (1972).
G. I. Taylor,The Scientific Papers of G. I. Taylor: III Aerodynamics and the Mechanics of Projectiles and Explosions, G. K. Batchelor, ed. (Cambridge University Press, Cambridge, 1963), pp. 493ff, 510ff; G. I. Taylor,Proc. Roy. Soc. A 101:159, 175 (1950).
J. Fineberg and V. Steinberg,Phys. Rev. Lett. 58:1332 (1987).
R. B. Griffiths,J. Chem. Phys. 60:195 (1974).
G. Dee and J. S. Langer,Phys. Rev. Lett. 50:383 (1983).
E. Ben-Jacob, H. R. Brand, G. Dee, L. Kramer, and J. S. Langer,Physica 14D:348 (1985); W. van Saarloos,Phys. Rev. Lett. 58:2571 (1987).
J. S. Patel, T. M. Leslie and J. W. Goodby,Ferroelectrics 59:137 (1984).
J. Bechhoeffer, Private communication.
M. Hara, H. Takezoe, and A. Fukuda,Japan. J. Appl. Phys. 25:1756 (1986); G. J. Kruger,Phys. Rep. 82C:249 (1982).
J. Q. Broughton, G. H. Gilmer, and K. A. Jackson,Phys. Rev. Lett. 49:1496 (1982).
M. O. Thompson, P. H. Bucksbaum, and J. Bokor, inEnergy Beam-Solid Interactions and Transient Thermal Processing, D. K. Biegelsen, G. A. Rozgonyi, and C. V. Shank, eds. (Elsevier, 1985), p. 181.
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This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems.
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Cladis, P.E. A dynamical test of phase transition order: New things in old places or old wine in new bottles. J Stat Phys 62, 899–925 (1991). https://doi.org/10.1007/BF01128168
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DOI: https://doi.org/10.1007/BF01128168