J. Phys. Soc. Jpn. 90, 124003 (2021) [11 Pages]
FULL PAPERS

Two-Dimensional Spin Model Possibly Undergoing a Phase Transition: Heisenberg Model of Headless Spins Preferring Twist on Triangular Lattice

+ Affiliations
Department of Chemistry, Faculty of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8571, Japan

Numerical experiments on the Heisenberg model of headless spins are performed for the two-dimensional triangular lattice. The assumed model is with the two-body interaction preferring twisted alignment, which tends to exhibit sublattice order at the absolute zero. A possible phase transition is suggested based on prolonged Monte Carlo steps necessary for equilibration, a pronounced peak of heat capacity, and local violation of the sixfold symmetry inherent to the lattice. The entropy gain associated with the heat capacity peak implies that the transition accompanies the disordering over three spin orientations defined locally.

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References

  • 1 J. J. Binney, N. J. Dowrick, A. J. Fisher, and M. E. J. Newman, The Theory of Critical Phenomena (Oxford University Press, New York, 1992). CrossrefGoogle Scholar
  • 2 H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford University Press, New York, 2010) CrossrefGoogle Scholar
  • 3 J. A. Pople and F. E. Karasz, J. Phys. Chem. Solids 18, 28 (1961). 10.1016/0022-3697(61)90080-4 CrossrefGoogle Scholar
  • 4 F. E. Karasz and J. A. Pople, J. Phys. Chem. Solids 20, 294 (1961). 10.1016/0022-3697(61)90017-8 CrossrefGoogle Scholar
  • 5 L. M. Amzel and L. N. Becka, J. Phys. Chem. Solids 30, 521 (1969) [Errata 30, 2495 (1969)]. 10.1016/0022-3697(69)90008-0 CrossrefGoogle Scholar
  • 6 Y. Nakazawa, Y. Yamamura, S. Kutsumizu, and K. Saito, J. Phys. Soc. Jpn. 81, 094601 (2012). 10.1143/JPSJ.81.094601 LinkGoogle Scholar
  • 7 C. Dressel, F. Liu, M. Prehm, X. Zeng, G. Ungar, and C. Tschierske, Angew. Chem., Int. Ed. 53, 13115 (2014). 10.1002/anie.201406907 CrossrefGoogle Scholar
  • 8 K. Saito, Y. Yamamura, Y. Miwa, and S. Kutsumizu, Phys. Chem. Chem. Phys. 18, 3280 (2016). 10.1039/C5CP06658A CrossrefGoogle Scholar
  • 9 K. Saito, M. Hishida, and Y. Yamamura, J. Phys. Soc. Jpn. 86, 084602 (2017). 10.7566/JPSJ.86.084602 LinkGoogle Scholar
  • 10 J. Fröhlich, B. Simon, and T. Spencer, Commun. Math. Phys. 50, 79 (1976). 10.1007/BF01608557 CrossrefGoogle Scholar
  • 11 P. G. de Genne and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, U.K., 1993) 3rd ed. Google Scholar
  • 12 P. A. Lebwohl and Q. Lasher, Phys. Rev. A 6, 426 (1972). 10.1103/PhysRevA.6.426 CrossrefGoogle Scholar
  • 13 H. Meirovitch, Chem. Phys. 21, 251 (1977). 10.1016/0301-0104(77)80019-0 CrossrefGoogle Scholar
  • 14 C. Dasgupta and B. I. Halperin, Phys. Rev. Lett. 47, 1556 (1981). 10.1103/PhysRevLett.47.1556 CrossrefGoogle Scholar
  • 15 L. Onsager, Phys. Rev. 65, 117 (1944). 10.1103/PhysRev.65.117 CrossrefGoogle Scholar
  • 16 P. C. Hohenberg, Phys. Rev. 158, 383 (1967). 10.1103/PhysRev.158.383 CrossrefGoogle Scholar
  • 17 N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966). 10.1103/PhysRevLett.17.1133 CrossrefGoogle Scholar
  • 18 J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973). 10.1088/0022-3719/6/7/010 CrossrefGoogle Scholar
  • 19 J. M. Kosterlitz, J. Phys. C 7, 1046 (1974). 10.1088/0022-3719/7/6/005 CrossrefGoogle Scholar
  • 20 C. Chiccoli, P. Pasini, and C. Zannoni, Physica A 148, 298 (1988). 10.1016/0378-4371(88)90148-3 CrossrefGoogle Scholar
  • 21 H. Kunz and G. Zumbach, Phys. Rev. B 46, 662 (1992). 10.1103/PhysRevB.46.662 CrossrefGoogle Scholar
  • 22 E. Mondal and S. K. Roy, Phys. Lett. A 312, 397 (2003). 10.1016/S0375-9601(03)00576-0 CrossrefGoogle Scholar
  • 23 S. Dutta and S. K. Roy, Phys. Rev. E 70, 066125 (2004). 10.1103/PhysRevE.70.066125 CrossrefGoogle Scholar
  • 24 R. Paredes V., A. I. Fariñas-Sánchez, and R. Botet, Phys. Rev. E 78, 051706 (2008). 10.1103/PhysRevE.78.051706 CrossrefGoogle Scholar
  • 25 Y. Tomita, Phys. Rev. E 90, 032109 (2014). 10.1103/PhysRevE.90.032109 CrossrefGoogle Scholar
  • 26 W. Maier and A. Saupe, Z. Naturforsch. A 13, 564 (1958). 10.1515/zna-1958-0716 CrossrefGoogle Scholar
  • 27 Z. Zhang, O. G. Mouritsen, and M. J. Zuckermann, Phys. Rev. Lett. 69, 2803 (1992). 10.1103/PhysRevLett.69.2803 CrossrefGoogle Scholar
  • 28 Z. Zhang, M. J. Zuckermann, and O. G. Mouritsen, Mol. Phys. 80, 1195 (1993). 10.1080/00268979300102981 CrossrefGoogle Scholar
  • 29 N. V. Priezjev and R. A. Pelcovits, Phys. Rev. E 64, 031710 (2001). 10.1103/PhysRevE.64.031710 CrossrefGoogle Scholar
  • 30 N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953). 10.1063/1.1699114 CrossrefGoogle Scholar
  • 31 M. Matsumoto and T. Nishimura, ACM Trans. Modeling Comput. Simulation 8, 3 (1998). 10.1145/272991.272995 CrossrefGoogle Scholar
  • 32 H. Park, Phys. Rev. B 49, 12881 (1994). 10.1103/PhysRevB.49.12881 CrossrefGoogle Scholar
  • 33 D. Stauffer, Phys. Rep. 54, 1 (1979). 10.1016/0370-1573(79)90060-7 CrossrefGoogle Scholar
  • 34 M. F. Sykes and J. W. Essam, J. Math. Phys. 5, 1117 (1964). 10.1063/1.1704215 CrossrefGoogle Scholar
  • 35 G. André, R. Bidaux, J.-P. Carton, R. Conte, and L. De Seze, J. Phys. (Paris) 40, 479 (1979). 10.1051/jphys:01979004005047900 CrossrefGoogle Scholar
  • 36 J. Villain, R. Bidaux, J.-P. Carton, and R. Conte, J. Phys. (Paris) 41, 1263 (1980). 10.1051/jphys:0198000410110126300 CrossrefGoogle Scholar