J. Phys. Soc. Jpn. 92, 054003 (2023) [9 Pages]
FULL PAPERS

Three-Step Ordering of Classical Headless Spins Preferring Twists on Icositetrachoric Honeycomb, a Four-Dimensional Analog of the Triangular Lattice

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

Four-dimensional space-filling by regular icositetrachorons (24-cell) results in a rare example of highly symmetric tripartite lattices. Assuming the interaction preferring mutual twists, Monte Carlo simulations of classical headless spins on its sites yielded four phases: disordered, nematic (axially symmetric), threefold-symmetric, and biaxially disordered phases with decreasing temperature. The ordering behavior is discussed while comparing the behavior of the same model on the triangular lattice with/without external fields. The biaxial phase is compatible with the ground-state spin configurations with the absolute minimum of interaction without frustrations. The phase diagram covering a region of merely the nematic order is presented.

©2023 The Physical Society of Japan

References

  • 1 H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1971). Google Scholar
  • 2 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
  • 3 H. Nishimori and G. Ortiz, Elements of Phase Transitions and Critical Phenomena (Oxford University Press, New York, 2010). CrossrefGoogle Scholar
  • 4 L. Onsager, Phys. Rev., Ser. II 65, 117 (1944). 10.1103/PhysRev.65.117 CrossrefGoogle Scholar
  • 5 R. Peierls, Math. Proc. Cambridge Philos. Soc. 32, 477 (1936). 10.1017/S0305004100019174 CrossrefGoogle Scholar
  • 6 R. Peierls, Proc. R. Soc. London, Ser. A 154, 207 (1936). 10.1098/rspa.1936.0047 CrossrefGoogle Scholar
  • 7 J. M. Luttinger, Phys. Rev., Ser. II 81, 1015 (1951). 10.1103/PhysRev.81.1015 CrossrefGoogle Scholar
  • 8 G. H. Wannier, Phys. Rev., Ser. II 79, 357 (1950). 10.1103/PhysRev.79.357 CrossrefGoogle Scholar
  • 9 G. H. Wannier, Phys. Rev. B 7, 5017 (1973). 10.1103/PhysRevB.7.5017 CrossrefGoogle Scholar
  • 10 A. P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994). 10.1146/annurev.ms.24.080194.002321 CrossrefGoogle Scholar
  • 11 A. D. Beath and D. H. Ryan, Phys. Rev. B 73, 174416 (2006). 10.1103/PhysRevB.73.174416 CrossrefGoogle Scholar
  • 12 R. Stübel and W. Janke, Phys. Rev. B 98, 174413 (2018). 10.1103/PhysRevB.98.174413 CrossrefGoogle Scholar
  • 13 M. J. Harris, S. T. Bramwell, D. F. McMorrow, T. Zeiske, and K. W. Godfrey, Phys. Rev. Lett. 79, 2554 (1997). 10.1103/PhysRevLett.79.2554 CrossrefGoogle Scholar
  • 14 K. Saito, M. Hishida, and Y. Yamamura, J. Phys. Soc. Jpn. 90, 124003 (2021). 10.7566/JPSJ.90.124003 LinkGoogle Scholar
  • 15 K. Saito and Y. Yamamura, J. Phys. Soc. Jpn. 91, 104603 (2022). 10.7566/JPSJ.91.104603 LinkGoogle Scholar
  • 16 H. S. M. Coxeter, Regular Polytopes (Dover, New York, 1973). Google Scholar
  • 17 I. Syôzi, Prog. Theor. Phys. 6, 306 (1951). 10.1143/ptp/6.3.306 CrossrefGoogle Scholar
  • 18 O. A. Petrenko and D. McK. Paul, Phys. Rev. B 63, 024409 (2000). 10.1103/PhysRevB.63.024409 CrossrefGoogle Scholar
  • 19 T. Yoshioka, A. Koga, and N. Kawakami, J. Phys. Soc. Jpn. 73, 1805 (2004). 10.1143/JPSJ.73.1805 LinkGoogle Scholar
  • 20 H. Park, Phys. Rev. B 49, 12881 (1994). 10.1103/PhysRevB.49.12881 CrossrefGoogle Scholar
  • 21 K. Saito and Y. Yamamura, J. Phys. Soc. Jpn. 91, 074007 (2022). 10.7566/JPSJ.91.074007 LinkGoogle Scholar
  • 22 P. C. Hohenberg, Phys. Rev. 158, 383 (1967). 10.1103/PhysRev.158.383 CrossrefGoogle Scholar
  • 23 N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966). 10.1103/PhysRevLett.17.1133 CrossrefGoogle Scholar
  • 24 K. Saito, M. Hishida, and Y. Yamamura, J. Phys. Soc. Jpn. 86, 084602 (2017). 10.7566/JPSJ.86.084602 LinkGoogle Scholar
  • 25 W. Maier and A. Saupe, Z. Naturforsch. A 13, 564 (1958). 10.1515/zna-1958-0716 CrossrefGoogle Scholar
  • 26 P. G. de Genne and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, U.K., 1993) 3rd ed. Google Scholar
  • 27 P. A. Lebwohl and Q. Lasher, Phys. Rev. A 6, 426 (1972). 10.1103/PhysRevA.6.426 CrossrefGoogle Scholar
  • 28 H. Meirovitch, Chem. Phys. 21, 251 (1977). 10.1016/0301-0104(77)80019-0 CrossrefGoogle Scholar
  • 29 J. M. Kosterlitz and D. J. Thouless, J. Phys. C 6, 1181 (1973). 10.1088/0022-3719/6/7/010 CrossrefGoogle Scholar
  • 30 J. M. Kosterlitz, J. Phys. C 7, 1046 (1974). 10.1088/0022-3719/7/6/005 CrossrefGoogle Scholar
  • 31 C. Chiccoli, P. Pasini, and C. Zannoni, Physica A 148, 298 (1988). 10.1016/0378-4371(88)90148-3 CrossrefGoogle Scholar
  • 32 H. Kunz and G. Zumbach, Phys. Rev. B 46, 662 (1992). 10.1103/PhysRevB.46.662 CrossrefGoogle Scholar
  • 33 E. Mondal and S. K. Roy, Phys. Lett. A 312, 397 (2003). 10.1016/S0375-9601(03)00576-0 CrossrefGoogle Scholar
  • 34 S. Dutta and S. K. Roy, Phys. Rev. E 70, 066125 (2004). 10.1103/PhysRevE.70.066125 CrossrefGoogle Scholar
  • 35 R. Paredes V., A. I. Fariñas-Sánchez, and R. Botet, Phys. Rev. E 78, 051706 (2008). 10.1103/PhysRevE.78.051706 CrossrefGoogle Scholar
  • 36 Y. Tomita, Phys. Rev. E 90, 032109 (2014). 10.1103/PhysRevE.90.032109 CrossrefGoogle Scholar
  • 37 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
  • 38 M. Matsumoto and T. Nishimura, ACM Trans. Modeling Comput. Simulation 8, 3 (1998). 10.1145/272991.272995 CrossrefGoogle Scholar
  • 39 K. Binder and D. P. Landau, Phys. Rev. B 30, 1477 (1984). 10.1103/PhysRevB.30.1477 CrossrefGoogle Scholar
  • 40 J. Lee and J. M. Kosterlitz, Phys. Rev. B 43, 3265 (1991). 10.1103/PhysRevB.43.3265 CrossrefGoogle Scholar
  • 41 L. D. Landau and E. M. Lifshitz, Statistical Physics (Butterworth-Heinemann, Oxford, U.K., 1980) 3rd ed. Google Scholar
  • 42 J.-C. Tolédano and P. Tolédano, The Landau Theory of Phase Transitions (World Scientific, Singapore, 1987). CrossrefGoogle Scholar
  • 43 J. Villain, R. Bidaux, J.-P. Carton, and R. Conte, J. Phys. (Paris) 41, 1263 (1980). 10.1051/jphys:0198000410110126300 CrossrefGoogle Scholar