Invaded cluster algorithm for critical properties of periodic and aperiodic planar Ising models

Journal of Physics A: Mathematical and General

Volumn 33, Issue 16, 2000, Pages 3097-3109

  Redner, Oliver ^a   Baake, Michael ^a  

^a UNIVERSITY OF TÜBINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040807550     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/33/16/304     Document Type: Article

References (40)

1. Ammann R, Grünbaum B and Shephard G 1992 Aperiodic tiles Discrete Comput. Geom. 8 1-25
2. Baake M 2001 A guide to mathematical quasicrystals Quasicrystals ed J-B Suck, M Schreiber and P Häußler (Berlin: Springer) to be published (Baake M 1999 Preprint math-ph/9901014)
3. Baake M 2001 A guide to mathematical quasicrystals Quasicrystals ed J-B Suck, M Schreiber and P Häußler (Berlin: Springer) to be published (Baake M 1999 Preprint math-ph/9901014)
4. Baake M, Grimm U and Baxter R J 1994 A critical Ising model on the Labyrinth Int. J. Mod. Phys. B 8 3579-600
5. Baake M, Grimm U, Repetowicz P and Joseph D 1998 Coordination sequences and critical points Proc. Int. Conf. on Quasicrystals (Tokyo) vol 6, ed S Takeuchi and T Fujiwara (Singapore: World Scientific) pp 124-7 (Baake M, Grimm U, Repetowicz P and Joseph D 1998 Preprint cond-mat/9809110)
6. Baake M, Grimm U, Repetowicz P and Joseph D 1998 Coordination sequences and critical points Proc. Int. Conf. on Quasicrystals (Tokyo) vol 6, ed S Takeuchi and T Fujiwara (Singapore: World Scientific) pp 124-7 (Baake M, Grimm U, Repetowicz P and Joseph D 1998 Preprint cond-mat/9809110)
7. Baake M, Klitzing R and Schlottmann M 1992 Fractally shaped acceptance domains of quasiperiodic square-triangle tilings with dodecagonal symmetry Physica A 191 554-8
8. Baake M, Kramer P, Schlottmann M and Zeidler D 1990 Planar patterns with fivefold symmetry as sections of periodic structures in 4-space Int. J. Mod. Phys. B 4 2217-68
9. Barber M N 1983 Finite-size scaling Phase Transitions and Critical Phenomena vol 8, ed C Domb and J L Lebowitz (London: Academic) pp 146-266
10. Beenker F P M 1982 Algebraic theory of non-periodic tilings of the plane by two simple building blocks: a square and a rhombus Techn. Univ. Eindhoven TH-Report 82-WSK-04
11. Bhattacharjee S M, Ho J-S and Johnson J A Y 1987 Translational invariance in critical phenomena: Ising model on a quasi-lattice J. Phys. A: Math. Gen. 20 4439-48
12. Binder K 1981 Finite size scaling analysis of Ising model block distribution functions Z. Phys. B 43 119-40
13. Briggs K 1993 Self-avoiding walks on quasilattices Int. J. Mod. Phys. B 7 1569-75
14. Choi Y S, Machta J, Tamayo P and Chayes L X 1999 Parallel invaded cluster algorithm for the Ising model Int. J. Mod. Phys. C 10 1-16
15. Dotsenko V 1995 Critical phenomena and quenched disorder Phys. Usp. 38 457-96 (Dotsenko V 1995 Usp. Fiz. Nauk. 165 287-96 (in Russian))
16. Dotsenko V 1995 Critical phenomena and quenched disorder Phys. Usp. 38 457-96 (Dotsenko V 1995 Usp. Fiz. Nauk. 165 287-96 (in Russian))
17. Franzese G, Cataudella V and Coniglio A 1998 Invaded cluster dynamics for frustrated models Phys. Rev. E 57 88-93
18. Grimm U and Baake M 1997 Aperiodic Ising models The Mathematics of Long-Range Aperiodic Order ed R V Moody (Dordrecht: Kluwer) pp 199-237
19. Harris A 1974 Effect of random defects on the critical behaviour of Ising models J. Phys. C: Solid State Phys. 7 1671-92
20. Hermisson J 2000 Aperiodic and correlated disorder in XY-chains: exact results J. Phys. A: Math. Gen. 33 57-69
21. Hermisson J 1999 Aperiodische Ordnung und magnetische Phasenübergänge PhD Thesis (Aachen: Shaker-Verlag)
22. Hermisson J 1999 Renormalization of two-dimensional Ising systems with irrelevant, marginal and relevant aperiodic (dis)order Mat. Sci. Eng. A at press
23. Hermisson J, Grimm U and Baake M 1997 Aperiodic Ising quantum chains J. Phys. A: Math. Gen. 30 7315-35
24. Ledue D, Landau D P and Teillet J 1995 Static critical behaviour of the ferromagnetic Ising model on the quasiperiodic octagonal tiling Phys. Rev. B 51 15 523-30
25. Luck J M 1993 A classification of critical phenomena on quasi-crystal s and other aperiodic structures Europhys. Lett. 359-64
26. Machta J 1998 Private communication
27. Machta J, Choi Y S, Lucke A, Schweizer T and Chayes L M 1995 Invaded cluster algorithm for equilibrium critical points Phys. Rev. Lett. 75 2792-5
28. Machta J, Choi Y S, Lucke A, Schweizer T and Chayes L M 1996 Invaded cluster algorithm for Potts models Phys. Rev. E 54 1332-45
29. Moriarty K, Machta J and Chayes L Y 1999 Dynamic and static properties of the invaded cluster algorithm Phys. Rev. E 59 1425-34
30. Okabe Y and Niizeki K 1988 Monte Carlo simulation of the Ising model on the Penrose lattice J. Phys. Soc. Japan 57 16-9
31. Penrose R 1974 The rôle of aesthetics in pure and applied mathematical research Bull. Int. Math. Appl. 10 266-71
32. Redner O 1999 Effiziente Simulation periodischer und nicht-periodischer Ising-Modelle am kritischen Punkt Diploma Thesis University of Tübingen (available from the author)
33. Repetowicz P, Grimm U and Schreiber M 1999 High-temperature expansion for Ising models on quasiperiodic tilings J. Phys. A: Math. Gen. 32 4397-418
34. Repetowicz P, Grimm U and Schreiber M 1999 Planar quasiperiodic Ising models Mat. Sci. Eng. A at press (Repetowicz P, Grimm U and Schreiber M 1999 Preprint cond-mat/9908088)
35. Repetowicz P, Grimm U and Schreiber M 1999 Planar quasiperiodic Ising models Mat. Sci. Eng. A at press (Repetowicz P, Grimm U and Schreiber M 1999 Preprint cond-mat/9908088)
36. Sire C, Mosseri R and Sadoc J-F 1989 Geometric study of a 2D tiling related to the octagonal quasiperiodic tiling J. Physique 50 3463-76
37. Sørensen E S, Jarić M V and Ronchetti M 1991 Ising model on Penrose lattices: boundary conditions Phys. Rev. B 44 9271-82
38. Swendsen R H and Wang J-S 1987 Nonuniversal critical dynamics in Monte Carlo simulations Phys. Rev. Lett. 58 86-8
39. Syozi I 1972 Transformation of Ising models Phase Transitions and Critical Phenomena vol 1, ed C Domb and M S Green (London: Academic) pp 269-329
40. Wolff U 1989 Collective Monte Carlo updating for spin systems Phys. Rev. Lett. 62 361-4