| CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES |
|
|
|
|
Partial Order in Potts Models on the Generalized Decorated Square Lattice |
| QIN Ming-Pu1, CHEN Jing1, CHEN Qiao-Ni2, XIE Zhi-Yuan1, KONG Xin1, ZHAO Hui-Hai1, Bruce Normand3, XIANG Tao1** |
1Institute of Physics, Chinese Academy of Sciences, Beijing 100190
2Department of Chemistry, Frick Laboratory, Princeton University, Princeton, New Jersey 08544, USA
3Department of Physics, Renmin University of China, Beijing 100872
|
|
| Cite this article: |
|
QIN Ming-Pu, CHEN Jing, CHEN Qiao-Ni et al 2013 Chin. Phys. Lett. 30 076402 |
|
|
|
|
Abstract We explore the Potts model on the generalized decorated square lattice, with both nearest (J1) and next-nearest (J2) neighbor interactions. Using the tensor renormalization-group method augmented by higher order singular value decompositions, we calculate the spontaneous magnetization of the Potts model with q = 2, 3, and 4. The results for q = 2 allow us to benchmark our numerics using the exact solution. For q = 3, we find a highly degenerate ground state with partial order on a single sublattice, but with vanishing entropy per site, and we obtain the phase diagram as a function of the ratio J2/J1. There is no finite-temperature transition for the q = 4 case when J1 = J2, whereas the magnetic susceptibility diverges as the temperature goes to zero, showing that the model is critical at T = 0.
|
|
|
Received: 28 April 2013
Published: 21 November 2013
|
|
| PACS: |
64.60.Cn
|
(Order-disorder transformations)
|
| |
05.50.+q
|
(Lattice theory and statistics)
|
| |
75.10.Hk
|
(Classical spin models)
|
| |
64.60.F-
|
(Equilibrium properties near critical points, critical exponents)
|
|
|
|
|
|
[1] Wu F Y 1982 Rev. Mod. Phys. 54 235
[2] Salas J and Sokal A D 1997 J. Stat. Phys. 86 551
[3] Kotecky R, Salas J and Sokal A D 2008 Phys. Rev. Lett. 101 030601
[4] Chen Q N, Qin M P, Chen J, Wei Z C, Zhao H H, Normand B and Xiang T 2011 Phys. Rev. Lett. 107 165701
[5] Deng Y J, Huang Y, Jacobsen J L, Salas J and Sokal A D 2011 Phys. Rev. Lett. 107 150601
[6] Diep H T and Debauche M 1991 Phys. Rev. B 43 8759
[7] Lipowski A and Horiguchi T 1995 J. Phys. A 28 3371
[8] Quartu R and Diep H T 1997 Phys. Rev. B 55 2975
[9] Wu F Y 1980 J. Stat. Phys. 23 773
[10] Matsuda Y, Kasai Y and Syozi I 1981 Prog. Theor. Phys. 65 1091
[11] Hajdukovic D 1983 J. Phys. A 16 2881
[12] Nightingale M P and Schick M 1982 J. Phys. A 15 L39
[13] Den Nijs M P M, Nightingale M P and Schick M 1982 Phys. Rev. B 26 2490
[14] Racz Z and Vicsek T 1983 Phys. Rev. B 27 2992
[15] Reed P 1985 J. Phys. C 18 L901
[16] Ferreira S J and Sokal A D 1999 J. Stat. Phys. 96 461
[17] Debauche M, Diep H T, Azaria P and Giacomini H 1991 Phys. Rev. B 44 2369
[18] Azaria P, Diep H T and Giacomini H 1987 Phys. Rev. Lett. 59 1629
[19] Zhao Y, Li W, Xi B, Zhang Z, Yan X, Ran S J, Liu T and Su G 2013 Phys. Rev. E 87 032151
[20] Levin M and Nave C P 2003 Phys. Rev. Lett. 90 120601
[21] Zhao H H, Xie Z Y, Chen Q N, Wei Z C, Cai J W and Xiang T 2010 Phys. Rev. B 81 174411
[22] Grest G S and Banavar J R 1981 Phys. Rev. Lett. 46 1458
[23] Xie Z Y, Chen J, Qin M P, Zhu J W, Yang L P and Xiang T 2012 Phys. Rev. B 86 045139
[24] Xie Z Y, Jiang H C, Chen Q N, Weng Z Y and Xiang T 2009 Phys. Rev. Lett. 103 160601
[25] Vidal G 2007 Phys. Rev. Lett. 98 070201
[26] Vidal G 2007 Phys. Rev. B 76 155117
[27] De Queiroz S L A, Paiva T, De Sa Martins J S and Dos Santos R R 1999 Phys. Rev. E 59 2772
[28] Wannier G H 1950 Phys. Rev. 79 357
[29] Stephenson J 1970 J. Math. Phys. 11 413
[30] Moore C and Newman M E J 2000 J. Stat. Phys. 99 629 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
