Triangular anisotropies in driven diffusive systems: Reconciliation of up and down

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

Volumn 60, Issue 3, 1999, Pages 2710-2715

  Rutenberg, A D ^a   Yeung, C ^b  

^a MCGILL UNIVERSITY   (Canada)

^b BEHREND COLLEGE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001143830     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/physreve.60.2710     Document Type: Article

References (18)

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2. H. K. Janssen and B. Schmittmann, Z. Phys. B 64, 503 (1986); K.-t. Leung and J. Cardy, J. Stat. Phys. 44, 567 (1986); 45, 1087 (1986).
3. H. K. Janssen and B. Schmittmann, Z. Phys. B 64, 503 (1986); K.-t. Leung and J. Cardy, J. Stat. Phys. 44, 567 (1986); 45, 1087 (1986).
4. H. K. Janssen and B. Schmittmann, Z. Phys. B 64, 503 (1986); K.-t. Leung and J. Cardy, J. Stat. Phys. 44, 567 (1986); 45, 1087 (1986).
5. In d=2 see K.-t. Leung, Phys. Rev. Lett. 66, 453 (1991); J.-S. Wang, J. Stat. Phys. 82, 1409 (1996); in d=3 see K.-t. Leung and J.-S. Wang, e-print cond-mat/9805285.
6. In d=2 see K.-t. Leung, Phys. Rev. Lett. 66, 453 (1991); J.-S. Wang, J. Stat. Phys. 82, 1409 (1996); in d=3 see K.-t. Leung and J.-S. Wang, e-print cond-mat/9805285.
7. c(∞). Indeed, while simulations of critical phenomena with E=∞ [3] are consistent with the coarse-grained field-theoretic results with a finite field, some debate remains [5,6]. Our resolution is simple: we restrict ourselves to finite fields.
8. J. Marro, A. Achahbar, P. L. Garrido, and J. J. Alonso, Phys. Rev. E 53, 6038 (1996); see related response by K.-t. Leung and R. K. P. Zia, J. Stat. Phys. 83, 1219 (1996).
9. J. Marro, A. Achahbar, P. L. Garrido, and J. J. Alonso, Phys. Rev. E 53, 6038 (1996); see related response by K.-t. Leung and R. K. P. Zia, J. Stat. Phys. 83, 1219 (1996).
10. P. L. Garrido, F. de los Santos, and M. A. Muñoz, Phys. Rev. E 57, 752 (1998); F. de los Santos and P. L. Garrido, e-print cond-mat/9805211.
11. I. M. Lifshitz and V. V. Slyozov, J. Phys. Chem. Solids 19, 35 (1961).
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14. Larger fields, above around 2 in our units, suppress the triangular anisotropy in both lattice and coarse-grained approaches [R. K. P. Zia (private communication)]. However, if the anisotropy is not strictly zero, questions about its sign remain.
15. By eye, rotating the field π/4 with respect to the lattice axes induces an anisotropy reversal.
16. K. Kitahara, Y. Oono, and D. Jasnow, Mod. Phys. Lett. B 6, 765 (1988).
17. C. Yeung, T. Rogers, A. Hernández-Machado, and D. Jasnow, J. Stat. Phys. 66, 1701 (1992).
18. We do not cover the entire phase space of deterministic coarse-grained models. In general, one requires a fully anisotropic surface tension, which can be selected by higher-order gradients in Eq. (2). One also can require a fully anisotropic particle mobility, rather than the simple elliptical anisotropy of Eq. (5), with more general order-parameter dependence as well.