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In this work the results of the study on a generalization of the XY model with an additional q-fold nematic-like term through Monte Carlo simulations in two dimensions (2D) have been presented. While the conventional 2D XY model has only integer vortexes, the generalized 2D XY model has both integer and non-integer 1/q vortexes, making the phase diagram of the generalized 2D XY model is much richer than that of the conventional 2D XY model. Here, we located the phase transition between the disordered phase (P), the quasi-long-range order phase (F), and the nematic phase (N) for the case of q = 3. We provided the numerical evidence to clarify the N−F phase transition of either the first-ordered or second-ordered phase transition. The results showed that the N−F phase transition is the second-ordered, not the first-order phase transition.
No. 5, 2008, pp. 580031-580036, https://doi.org/10.1209/0295-5075/83/58003.
 A. B. Cairns, M. J. Cliffe, J. A. M. Paddison, D. Daisenberger et al., Encoding Complexity within Supramolecular Analogues of Frustrated Magnets, Nature Chemistry Vol. 8, 2016, pp. 442-447, https://doi.org/10.1038/nchem.2462.
 S. Romano, Topological Transitions in Two-Dimensional Lattice Spin Models, Physical Review E, Vol. 73, 2016, pp. 0427011-0427012, https://doi.org/10.1103/PhysRevE.73.042701.
 F´. C. Poderoso, J. J. Arenzon, Y. Levin, New Ordered Phases in a Class of Generalized XY Models, Physical Review Letters, Vol. 106, 2011, pp. 0672021-0672024, https://doi.org/10.1103/PhysRevLett.106.067202.
 Y. Shi, A. Lamacraft, P. Fendley, Boson Pairing and Unusual Criticality in a Generalized xy Model, Physical Review Letters, Vol. 107, 2011, pp. 2406011-2406015, https://doi.org/10.1103/PhysRevLett.107.240601.
 D. M. H¨ubscher, S. Wessel, Stiffness Jump in the Generalized xy Model on the Square Lattice, Physical Review E, Vol. 87, 2013, pp. 0621121-0621125, https://doi.org/10.1103/PhysRevE.87.062112.
 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.
 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.
 D. X. Nui, L. Tuan, N. D. T. Kien, P. T. Huy, D. T. Hung, D. X. Viet, Correlation Length in a Generalized Two-Dimensional XY Model, Physical Review B, Vol. 98, 2018, pp. 1444211-1444219, https://doi.org/10.1103/PhysRevB.98.144421.
 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.
 K. Kanki, D. Loison, and K.D. Schotte, Efficiency of the Microcanonical Over-relaxation Algorithm for Vector Spins Analyzing First and Second Order Transitions, The European Physical Journal B, Vol. 44, 2005,
pp. 309-315, https://doi.org/10.1140/epjb/e2005-00130-7.
 J. Imriska, Phase Diagram of a Modified XY Model, Bachelor’s Thesis, Comenius University in Bratislava, 2009.
 C. M. Lapilli, P. Pfeifer, C. Wexler, Universality Away from Critical Points in Two-Dimensional Phase Transitions, Physical Review Letters, Vol. 96, 2006, pp. 1406031-1406034, https://doi.org/10.1103/PhysRevLett.96.140603.
 D. X. Nui, Monte Carlo Study of KosterlitzThouless Phase Transition Phenomenon in the Generalized 2D XY Model, Ph.D. Thesis, Hanoi University of Science and Technology, 2020 (in Vietnamese).
 M. Nishino, S. Miyashita, Termination of the Berezinskii-Kosterlitz-Thouless Phase with a New Critical Universality in Spin-Crossover Systems, Physical Review B, Vol. 92, 2015, pp. 1844041-1844047, https://doi.org/10.1103/PhysRevB.92.184404.
 Y. Komura, Y. Okabe, Large-Scale Monte Carlo Simulation of Two-Dimensional Classical XY Model Using Multiple Gpus, Journal of the Physical Society of Japan, Vol. 81, 2012, pp. 1130011-1130014, https://doi.org/10.1143/JPSJ.81.113001.
 R. M. Liu, W. Z. Zhuo, J. Chen et al., Shkin-Teller Criticality and Weak First-Order Behavior of the Phase Transition to a Fourfold Degenerate State in Two-Dimensional Frustrated Ising Antiferromagnets, Physical Review E, Vol. 96, 2017, pp. 0121031-0121037, https://doi.org/10.1103/PhysRevE.96.012103.
 S. Sinha, S. K. Roy, Finite Size Scaling and First-Order Phase Transition in a Modified XY Model, Physical Review E, Vol. 81, 2010, pp. 0221021-0221024, https://doi.org/10.1103/PhysRevE.81.022102.