Binder Parameter in a Generalized Two-dimensional XY Model
Main Article Content
Abstract
We performed Monte Carlo simulation for a two-dimensional generalized XY model and calculated the magnetic and nematic Binder parameters. The phase diagram is re-examined based on these Binder parameters, demonstrating their power in studying generalized XY models. The Binder parameter has distinctive behaviors, resulting in different types of phase transition. More importantly, the magnetic Binder parameter gives more insights into the tricritical region where the Kosterlitz-Thouless, Ising, and 1/2 Kosterlitz-Thouless (KT) transition lines meet. It shows signatures for the intermediate region starting from the tricritical point, where the transition line is neither the same physics as the Ising transition below nor the KT transition far above the tricritical point.
Keywords:
Monte Carlo simulations, phase transitions, magnetic materials.
References
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[4] S. E. Korshunov, Possible Splitting of A Phase Transition in a 2D XY Model, JETP Letters, Vol. 41, 1985,
pp. 263-266, http://jetpletters.ru/ps/1444/article_21975.shtml.
[5] D. H. Lee, G. Grinstein, Strings in Two-dimensional Classical XY Models, Physical Review Letters, Vol. 55, 1985, pp. 541-544, https://doi.org/10.1103/PhysRevLett.55.541.
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[11] G. A. Canova, Y. Levin, J. J. Arenzon, Kosterlitz-Thouless and Potts Transitions in A Generalized XY Model, Physical Review E, Vol. 89, 2014, pp. 0121261-0121265, https://doi.org/10.1103/PhysRevE.89.012126.
[12] G. A. Canova, Y. Levin, J. J. Arenzon, Competing Nematic Interactions in A Generalized XY Model in Two and Three Dimensions, Physical Review E, Vol. 94, 2016, pp. 0321401-03214012, https://doi.org/10.1103/PhysRevE.94.032140.
[13] D. M. H¨ubscher, S. Wessel, Stiffness Jump in the Generalized XY Model on the Square Lattice, Phys. Physical Review E, Vol. 87, 2013, pp. 0621121-0621125, https://doi.org/10.1103/PhysRevE.87.062112.
[14] Y. Shi, A. Lamacraft, P. Fendley, B. Pairing, Unusual Criticality in a Generalized XY Model, Physical Review Letters, Vol. 107, 2011, pp. 2406011-2406015, https://doi.org/10.1103/PhysRevLett.107.240601.
[15] P. Serna, J. T. Chalker, P.Fendley, Deconfinement Transitions in a Generalised XY Model, Journal of Physics A: Mathematical and Theoretical, Vol. 50, 2017, pp. 4240031-42400319, https://doi.org/10.1088/1751-8121/aa89a1.
[16] T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, M. P. A. Fisher, Deconfined Quantum Critical Points,
Vol. 303, 2004, pp. 1490-1494, https://www.science.org/doi/10.1126/science.1091806.
[17] D. X. Nui, L. Tuan, N. D. T. Kien, P. T. Huy, H. T. Dang, D. X. Viet, Correlation Length In A Generalized Twodimensional XY Model, Physical Review B, Vol. 98, 2018, pp. 1444211-1444219, https://doi.org/10.1103/PhysRevB.98.144421.
[18] V. D. Touchette, P. P. Orth, P. Coleman, P. Chandra, T. C. Lubensky, Emergent Potts Order in a Coupled Hexatic-Nematic XY Model, Physical Review X, Vol. 12, 2022, pp. 0110431-01104322, https://doi.org/10.1103/PhysRevX.12.011043.
[19] D. Loison, Binder’s Cumulant for the Kosterlitz-Thouless Transition, Journal of Physics: Condensed Matter,
Vol. 11, 1999, pp. 401-406, https://doi.org/10.1088/0953-8984/11/34/101.
[20] M. Hasenbusch, The Binder Cumulant at the Kosterlitz–Thouless Transition, Journal of Statistical Mechanics: Theory and Experiment, Vol. 08, 2008, pp. 080031-0800321, https://doi.org/10.1088/1742-5468/2008/08/P08003.
[21] D. X. Viet, H. Kawamura, Monte Carlo Studies of Chiral and Spin Ordering of the Threedimensional Heisenberg Spin Glass, Physical Review B, Vol. 80, 2009, pp. 0644181-06441820, https://doi.org/10.1103/PhysRevB.80.064418.
[22] L. M. Tuan, T. T. Long, D. X. Nui, P. T. Minh, N. D. T. Kien, D. X. Viet, Binder Ratio in the Two-Dimensional Q-State Clock Model, Physical Review E, Vol. 106, 2022, pp. 0341381-0341388, https://doi.org/10.1103/PhysRevE.106.034138.
[23] U. Wolff, Collective Monte Carlo Updating for Spin Systems, Physical Review Letters, Vol. 62, 1989,
pp. 361-364, https://doi.org/10.1103/PhysRevLett.62.361.
[24] J. Imriska, Phase Diagram of a Modified XY Model, Bachelor’s Thesis, Comenius University in Bratislava, 2009.
[25] T. Surungan, Y. Okabe, Kosterlitz Thouless Transition in Planar Spin Models with Bond Dilution, Physical Review B, Vol. 71, 2005, pp. 1844381-1844387, https://doi.org/10.1103/PhysRevB.71.184438.