Abstract
A ϕ 4-model with symmetric double-well-like on-site potential and anharmonic, infinite range interactions is investigated. This model exhibits a first order phase transition at a temperature T c. The time-dependent displacement correlation function is studied in the framework of the mode coupling theory (MCT). Depending on the choice of slow modes, MCT makes qualitatively different predictions which are compared with MD-results. These numerical results suggest that only the order parameter mode {ie1-1} should be considered as slow. In that case it is shown that MCT yields a dynamical transition in the supercooled high-temperature phase {ie1-2} at a temperature T* which coincides with the spinodal temperature T s (T s = 0 for our model) where the metastable supercooled phase becomes instable.
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Riste, T., Samuelsen, E.J., Otnes, K., Feder, J.: Solid State Commun. 9, 1455 (1971)
Halperin, B.I., Varma, C.M.: Phys. Rev. B14, 4030 (1976)
Schwabl, F., Täuber, U.C.: Phys. Rev. B43, 11112 (1991)
Silberglitt, R.: Solid State Commun. 11, 247 (1972); Combs, G. J., Cowley, R.A.: J. Phys. C6,121 (1973); Murata, K.K.: Phys. Rev. B11, 462 (1975); Bausch, R., Halperin, B.I.: Phys. Rev. B18, 190 (1978)
Schneider, T., Stoll, E.: Phys. Rev. Lett. 31, 1254 (1975)
Schwabl, F.: Phys. Rev. Lett. 28, 500 (1972)
Aubry, S.: J. Chem. Phys. 62, 3217 (1976), ibid., 64, 3392 (1976); Krumhansl, J.A., Schrieffer, J.R.: Phys. Rev. B11, 3535 (1975); Varma, C.M.: Phys. Rev. B14,244 (1976)
Bruce, A.D., Cowley, R.A.: Adv. Phys. 29 (1) 111,219 (1980); Miller, K.A., Thomas, H. (eds) "Structural Phase Transitions", Vol. I and 11. Berlin, Heidelberg, New York: Springer
Götze, W. In: Hansen, J.P. Levesque, D., Zinn-Justin, J. (eds) "Liquids, freezing and the glass transition", North Holland, Amsterdam (1991); Götze, W., Sjögren, L.: Rep. Prog. Phys. 55, 241 (1992); Schilling, R. in Richert, R., Blumen, A. (eds) Disorder Effects on Relaxational Processes. Berlin, Heidelberg, New York: Springer 1994
Aksenov, V.L., Bobeth, M., Plakida, N.M., Schreiber, J.: J. Phys. C20, 375 (1987)
Michel, K.H.: Z. Phys. 68,259 (1987); Bostoen, C., Michel, K.H.: Z. Phys. 71, 369 (1988); Phys. Rev. B43, 4415 (1991)
Götze, W., Sjögren, L.: J. Phys. C17, 5759 (1984)
Kirkpatrick, T.R., Thirumalai, D.: Phys. Rev. B37, 5342 (1988); A37, 4439 (1988); B38, 4881 (1988)
Kirkpatrick, T.R., Thirumalai, D.: Phys. Rev. Lett. 58, 2091 (1987); Phys. Rev. B36, 5388 (1987)
Rostiashvili, V.G.: Physica A148, 208 (1988); Sov. Phys. JETP. 70, 563 (1990); Schweizer, K.S.: J. Chem. Phys. 91, 5802 (1989)
Aksenov, V.L., Bobeth, M., Plakida, N.M., Schreiber, J.: Z. Phys. B69, 393 (1987); Prigodin, V.N.: J. Phys. Condens. Matter 4, 785 (1992)
Flach, S.: Z. Phys. B82,419 (1991); Flach, S., Olbrich, E.: Z. Phys. B85, 99 (1991)
Kob, W., Schilling, R.: J. Phys. Condens. Matter 3, 9195 (1991)
Fischer, T.M., Schilling, R.: Z. Phys. B92, 67 (1993)
Binder, K., Young, A.P.: Rev. Mod. Phys. 58, 811 (1986) 415
Michel, K.H., Rowe, J.M.: Phys. Rev. B22,1417 (1980)
Forster, D.: Hydrodynamical Fluctuations, Broken Symmetry and Correlation Functions, Benjamin, New York (1975); Grabert, H.: Projection Operator Techniques in Nonequilibrium Statistical Mechanics, Springer Tracts in Modern Physics, vol. 95. Berlin, Heidelberg, New York: Springer 1982
Swope, W.C., Andersen, H.C., Berens, P.H. and Wilson, K.R.: J. Chem. Phys. 76, 637 (1982); Heermann, D.W.: Computer Simulation Methods in Theoretical Physics, Berlin: Springer 1986
Munakata, T.: J. Phys. Soc. Jpn. 60, 2800 (1991)
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Duering, E., Schilling, R. & Wittmann, HP. On the applicability of mode coupling theory to a ϕ 4-model with first order phase transition. Z. Phys. B 100, 409–415 (1997). https://doi.org/10.1007/s002570050140
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DOI: https://doi.org/10.1007/s002570050140