Soluble phase field model

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

Volumn 56, Issue 1 SUPPL. A, 1997, Pages 77-87

  Marini Bettolo Marconi, Umberto ^a,b,c   Crisanti, Andrea ^d   Iori, Giulia ^b  

^a UNIVERSITY OF CAMERINO   (Italy)

^b INFM   (Italy)

^c INFN SEZIONE DI PERUGIA   (Italy)

^d UNIVERSITÀ DI ROMA LA SAPIENZA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4243946779     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.56.77     Document Type: Article

References (31)

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24. The present spherical model defined by Eq. (26) is different from the O(n) spherical model discussed in previous papers [11]. In that case both the order parameter and the U field were vector fields coupled bilinearly. However, the two models in the infinite-volume limit and in the limit of infinite components generate identical equations for the average fields and their correlations, although the physical interpretation remains different for the two models.
25. Stanley has shown the equivalence of the spherical model and an n-component spin model in the limit of n → ∞ in the case of translationally invariant systems. H.E. Stanley, Phys. Rev. 76, 718 (1968).
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29. The equilibrium properties of interfaces have been studied in the mode-coupling approximation by U. Marini Bettolo Marconi and B.L. Gyorffy, Physica A 159, 221 (1989); Phys. Rev. A 41, 6732 (1990).
30. 2 term and U ø in Eq. (26) have not been chosen independently, as assumed in Ref. [11], but their ratio was fixed to guarantee the correct energy balance as explained in Sees. II and I.
31. Although the notion of a spinodal line signaling a sharp transition from a nucleation mechanism to a spinodal decomposition mechanism is not exact in systems with finite-range interactions and the transition is gradual, still the concept of spinodal has a heuristic value [see, for example, the article by Binder about spinodal decomposition: K. Binder, in Materials Science and Technology, edited by R.W. Cahn, P. Haasen, and E.J. Kramer (VCH, Weinheim, 1991)].