Checkerboards, stripes, and corner energies in spin models with competing interactions

Physical Review B - Condensed Matter and Materials Physics

Volumn 84, Issue 6, 2011, Pages

  Giuliani, Alessandro ^a   Lebowitz, Joel L ^b   Lieb, Elliott H ^c  

^a ROMA TRE UNIVERSITY   (Italy)

^b RUTGERS UNIVERSITY   (United States)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 80052386119     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.84.064205     Document Type: Article

References (62)

1. A. Giuliani, J. L. Lebowitz, and E. H. Lieb, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.064420 74, 064420 (2006). (Pubitemid 44291260)
2. A. Giuliani, J. L. Lebowitz, and E. H. Lieb, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.76.184426 76, 184426 (2007).
3. A. Giuliani, J. L. Lebowitz, and E. H. Lieb, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-008-0589-z 286, 163 (2009).
4. A. Giuliani, J. L. Lebowitz, and E. H. Lieb, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.134420 80, 134420 (2009).
5. P. Ball, The Self-Made Tapestry: Pattern Formation in Nature (Oxford University Press, New York, 2001).
6. J. Choi, J. Wu, C. Won, Y. Z. Wu, A. Scholl, A. Doran, T. Owens, and Z. Q. Qiu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.207205 98, 207205 (2007). (Pubitemid 47139540)
7. K. De'Bell, A. B. Mac Issac, and J. P. Whitehead, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.72.225 72, 225 (2000).
8. V. J. Emery and S. A. Kivelson, Phys. C (Amsterdam) PHYCE6 0921-4534 10.1016/0921-4534(93)90581-A 209, 597 (1993).
9. J. Maclennan and M. Seul, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.2082 69, 2082 (1992).
10. J. A. Robertson, S. A. Kivelson, E. Fradkin, A. C. Fang, and A. Kapitulnik, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.134507 74, 134507 (2006). (Pubitemid 44596200)
11. N. Saratz, A. Lichtenberger, O. Portmann, U. Ramsperger, A. Vindigni, and D. Pescia, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.077203 104, 077203 (2010).
12. M. Seul and D. Andelman, Science SCIEAS 0036-8075 10.1126/science.267. 5197.476 267, 476 (1995).
13. B. Spivak and S. A. Kivelson, Ann. Phys. (NY) APNYA6 0003-4916 10.1016/j.aop.2005.12.002 321, 2071 (2006). (Pubitemid 44159227)
14. A. D. Stoycheva and S. J. Singer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.4657 84, 4657 (2000).
15. J. Wu, J. Choi, C. Won, Y. Z. Wu, A. Scholl, A. Doran, Chanyong Hwang, and Z. Q. Qiu, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.014429 79, 014429 (2009).
16. S. Kondo and T. Miura, Science SCIEAS 0036-8075 10.1126/science.1179047 329, 1616 (2010).
17. A. M. Turing, Philos. Trans. R. Soc. London B PTRBAE 0962-8436 10.1098/rstb.1952.0012 237, 3 (1952).
18. S. A. Cannas, M. F. Michelon, D. A. Stariolo, and F. A. Tamarit, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.184425 73, 184425 (2006). (Pubitemid 43752527)
19. S. A. Pighin and S. A. Cannas, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.224433 75, 224433 (2007).
20. E. Rastelli, S. Regina, and A. Tassi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.144418 73, 144418 (2006). (Pubitemid 43572156)
21. R. Czech and J. Villain, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/1/3/013 1, 619 (1989).
22. M. Grousson, G. Tarjus, and P. Viot, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.62.7781 62, 7781 (2000). (Pubitemid 32088001)
23. U. Löw, V. J. Emery, K. Fabricius, and S. A. Kivelson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.72.1918 72, 1918 (1994).
24. A. B. MacIsaac, J. P. Whitehead, M. C. Robinson, and K. De'Bell, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.51.16033 51, 16033 (1995).
25. Z. Nussinov, e-print arXiv: cond-mat/0105253.
26. P. Politi, Comments Cond. Matter Phys. 18, 191 (1998).
27. A. DeSimone, R. V. Kohn, F. Otto, and S. Müller, in The Science of Hysteresis II: Physical Modeling, Micromagnetics, and Magnetization Dynamics, edited by, G. Bertotti, and, I. Mayergoyz, (Elsevier, New York, 2001), pp. 269-381.
28. C. B. Muratov, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-010- 1094-8 299, 45 (2010).
29. Ar. Abanov, V. Kalatsky, V. L. Pokrovsky, and W. M. Saslow, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.51.1023 51, 1023 (1995).
30. D. G. Barci and D. A. Stariolo, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.075437 79, 075437 (2009).
31. S. A. Brazovskii, Zh. Eksp. Teor. Fiz. 68, 175 (1975)
32. S. A. Brazovskii, [Sov. Phys. JETP 41, 85 (1975)].
33. A. B. Kashuba and V. L. Pokrovsky, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.48.10335 48, 10335 (1993).
34. V. J. Emery, E. Fradkin, S. A. Kivelson, and T. C. Lubensky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.2160 85, 2160 (2000).
35. J. Lorenzana, C. Castellani, and C. Di Castro, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.64.235127 64, 235127 (2001);
36. J. Lorenzana, C. Castellani, and C. Di Castro, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.64.235128 64, 235128 (2001).
37. C. B. Muratov, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.66.066108 66, 066108 (2002). (Pubitemid 40606048)
38. C. Ortix, J. Lorenzana, and C. Di Castro, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.246402 100, 246402 (2008).
39. O. Portmann, A. Golzer, N. Saratz, O. V. Billoni, D. Pescia, and A. Vindigni, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.82.184409 82, 184409 (2010).
40. P. C. Hohenberg and J. B. Swift, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.52.1828 52, 1828 (1995).
41. Y. Shiwa, J. Stat. Phys. JSTPBS 0022-4715 10.1007/s10955-006-9080-4 124, 1207 (2006). (Pubitemid 44581245)
42. F. Cinti, O. Portmann, D. Pescia, and A. Vindigni, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.214434 79, 214434 (2009).
43. G. A. Gehring and M. Keskin, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/5/44/007 5, L581 (1993).
44. A. Vindigni, N. Saratz, O. Portmann, D. Pescia, and P. Politi, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.092414 77, 092414 (2008).
45. B. Kaplan and G. A. Gehring, J. Magn. Magn. Mater. JMMMDC 0304-8853 10.1016/0304-8853(93)90863-W 128, 111 (1993).
46. Y. Yafet and E. M. Gyorgy, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.38.9145 38, 9145 (1988).
47. T. Garel and S. Doniach, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.26.325 26, 325 (1982).
48. E. Nielsen, R. N. Bhatt, and D. A. Huse, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.054432 77, 054432 (2008).
49. N. Abu-Libdeh and D. Venus, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.80.184412 80, 184412 (2009).
50. N. Abu-Libdeh and D. Venus, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.195416 81, 195416 (2010).
51. M. Grousson, G. Tarjus, and P. Viot, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3455 86, 3455 (2001). (Pubitemid 32380660)
52. O. Osenda, F. A. Tamarit, and S. A. Cannas, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.021114 80, 021114 (2009).
53. J. Schmalian and P. G. Wolynes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.836 85, 836 (2000).
54. J. Fröhlich, R. Israel, E. H. Lieb, and B. Simon, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/BF01940327 62, 1 (1978);
55. J. Fröhlich, R. Israel, E. H. Lieb, and B. Simon, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01014646 22, 297 (1980).
56. E. Edlund and M. Nilsson Jacobi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.137203 105, 137203 (2010).
57. R. Jamei, S. Kivelson, and B. Spivak, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.056805 94, 056805 (2005). (Pubitemid 40620877)
58. B. Spivak, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.67.125205 67, 125205 (2003).
59. B. Spivak and S. A. Kivelson, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.70.155114 70, 155114 (2004). (Pubitemid 40040413)
60. E. H. Lieb and M. Loss, Analysis. Second Edition (American Mathematical Society, Providence, RI, 2001).
61. R. Frank and E. H. Lieb, Calc. Variat. Partial Differ. Equations PRLTAO 0944-2669 10.1007/s00526-009-0302-x 39, 85 (2010).
62. J. L. Lebowitz and O. Penrose, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1704821 7, 98 (1966).