Geodesic
Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices
Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 3, pp. 441-452 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate low-temperature magnetization processes for two frustrated quantum Heisenberg antiferromagnets using the lattice gas model. The emerging discrete degrees of freedom indicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with a finite nearest-neighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation, we obtain analytic results for thermodynamically large systems in the one-dimensional case. In the two-dimensional case, we simulate systems of the size up to $100\times100$ sites using the classical Monte Carlo method.
Keywords: Heisenberg quantum antiferromagnet, frustrated lattice, magnetization process. 
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O. V. Derzhko; T. E. Krokhmalskii; J. Richter. Quantum Heisenberg antiferromagnet on low-dimensional frustrated lattices. Teoretičeskaâ i matematičeskaâ fizika, Tome 168 (2011) no. 3, pp. 441-452. http://geodesic.mathdoc.fr/item/TMF_2011_168_3_a6/

[1] A. Honecker, J. Phys.: Condens. Matter, 11:24 (1999), 4697–4713, arXiv: ; A. Honecker, J. Schulenburg, J. Richter, J. Phys.: Condens. Matter, 16:11 (2004), S749–S758, arXiv: ; J. Richter, J. Schulenburg, A. Honecker, “Quantum magnetism in two dimensions: From semi-classical Néel order to magnetic disorder”, Quantum Magnetism, Lecture Notes in Physics, 645, eds. U. Schollwöck, J. Richter, D. J. J. Farnell, R. F. Bishop, Springer, Berlin, 2004, 85–153 cond-mat/9902163cond-mat/0309425 | DOI | DOI | DOI

[2] J. Schnack, H.-J. Schmidt, J. Richter, J. Schulenburg, Eur. Phys. J. B, 24:4 (2001), 475–481, arXiv: ; J. Schulenburg, A. Honecker, J. Schnack, J. Richter, H.-J. Schmidt, Phys. Rev. Lett., 88:16 (2002), 167207, 4 pp., arXiv: ; J. Richter, J. Schulenburg, A. Honecker, J. Schnack, H.-J. Schmidt, J. Phys.: Condens. Matter, 16:11 (2004), S779–S784 ; J. Richter, ФНТ, 31:8–9 (2005), 918–928 ; O. Derzhko, J. Richter, A. Honecker, H.-J. Schmidt, ФНТ, 33:9 (2007), 982–996, arXiv: ; J. Richter, O. Derzhko, “Correlated systems on geometrically frustrated lattices: from magnons to electrons”, Condensed Matter Physics in the Prime of the 21st Century. Phenomena, Materials, Ideas, Methods, 43rd Karpacz Winter School of Theoretical Physics (La̧dek Zdrój, Poland, 5–11 February 2007), ed. J. Jȩdrzejewski, World Scientific, Singapore, 2008, 237–270 cond-mat/0108432cond-mat/0108498cond-mat/0612281 | DOI | DOI | DOI | DOI | DOI

[3] M. E. Zhitomirsky, H. Tsunetsugu, Phys. Rev. B, 70:10 (2004), 100403(R), 4 pp., arXiv: ; O. Derzhko, J. Richter, Phys. Rev. B, 70:10 (2004), 104415, 6 pp., arXiv: ; M. E. Zhitomirsky, H. Tsunetsugu, Progr. Theor. Phys. Suppl., 2005, no. 160, 361–382, arXiv: ; O. Derzhko, J. Richter, Eur. Phys. J. B, 52:1 (2006), 23–36, arXiv: cond-mat/0405578cond-mat/0404204cond-mat/0506327cond-mat/0604023 | DOI | DOI | DOI | DOI

[4] J. Richter, O. Derzhko, T. Krokhmalskii, Phys. Rev. B, 74:14 (2006), 144430, 5 pp., arXiv: ; O. Derzhko, J. Richter, T. Krokhmalskii, Acta Phys. Polon. A, 113:1 (2008), 433–436 cond-mat/0606806 | DOI | DOI

[5] O. Derzhko, T. Krokhmalskii, J. Richter, Phys. Rev. B, 82:21 (2010), 214412, 14 pp., arXiv: 1009.3828 | DOI

[6] A. Honecker, F. Mila, M. Troyer, Eur. Phys. J. B, 15:2 (2000), 227–233, arXiv: cond-mat/9910438 | DOI

[7] P. Chen, C.-Y. Lai, M.-F. Yang, Phys. Rev. B, 81:2 (2010), 020409(R), 4 pp., arXiv: 0910.5081 | DOI

[8] H.-J. Schmidt, J. Phys. A, 35:31 (2002), 6545–6555, arXiv: cond-mat/0203270 | DOI | MR | Zbl

[9] H.-J. Schmidt, J. Richter, R. Moessner, J. Phys. A, 39:34 (2006), 10673–10690, arXiv: cond-mat/0604649 | DOI | MR | Zbl

[10] E. Müller-Hartmann, J. Zittartz, Z. Phys. B, 27:3 (1977), 261–266 | DOI | MR

[11] X. N. Wu, F. Y. Wu, Phys. Lett. A, 144:3 (1990), 123–126 | DOI

[12] X.-Z. Wang, J. S. Kim, Phys. Rev. Lett., 78:3 (1997), 413–416 | DOI | MR | Zbl

[13] S. J. Penney, V. K. Cumyn, D. D. Betts, Physica A, 330:3–4 (2003), 507–518 | DOI | MR | Zbl

[14] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR

[15] D. J. J. Farnell, R. Zinke, J. Schulenburg, J. Richter, J. Phys.: Condens. Matter, 21:40 (2009), 406002, 12 pp., arXiv: 0908.2881 | DOI

[16] T. Ono, H. Tanaka, H. Aruga Katori, F. Ishikawa, H. Mitamura, T. Goto, Phys. Rev. B, 67:10 (2003), 104431, 7 pp. | DOI

[17] C. Schröder, H. Nojiri, J. Schnack, P. Hage, M. Luban, P. Kögerler, Phys. Rev. Lett., 94:1 (2005), 017205, 4 pp. | DOI

[18] M. Maksymenko, O. Derzhko, J. Richter, Acta Phys. Polon. A, 119:6 (2011), 860–862 ; Low-temperature properties of the quantum Heisenberg antiferromagnet on some one-dimensional lattices containing equilateral triangles, preprint ICMP-10-08E, Inst. Condens. Matter Phys., Lvov, 2010 {http://www.icmp.lviv.ua/preprints/2010.html} | DOI

[19] N. B. Ivanov, Cond. Matter Phys., 12:3 (2009), 435–447, arXiv: 0909.2182 | DOI

[20] G. Seeber, P. Kögerler, B. M. Kariuki, L. Cronin, Chem. Commun., 2004:11 (2004), 1580–1581 ; N. B. Ivanov, J. Schnack, R. Schnalle, J. Richter, P. Kögerler, G. N. Newton, L. Cronin, Y. Oshima, H. Nojiri, Phys. Rev. Lett., 105:3 (2010), 037206, 4 pp., arXiv: 1004.2373 | DOI | DOI

[21] J.-B. Fouet, F. Mila, D. Clarke, H. Youk, O. Tchernyshyov, P. Fendley, R. M. Noack, Phys. Rev. B, 73:21 (2006), 214405, 13 pp., arXiv: cond-mat/0603609 | DOI