Study on the critical properties of thin magnetic films using the clock model

Nguyen, T. L. H.; Ngo, V. Thanh

doi:10.1088/2043-6254/aa5981

Cited by 2 publications

(2 citation statements)

References 27 publications

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“…there are second-order phase transitions but they are no longer in the same universality class as the clock models [8][9][10][11][12]. There is also some evidence that these turn into BKT transitions at sufficiently small but positive ℎ 𝑞 [9,13], although there are others who disagree [14,15]. In this work, we study the model at finite ℎ 𝑞 using MC and TRG across a wide range of integer and noninteger 𝑞 to characterize the phase diagram.…”

Section: Pos(lattice2023)223mentioning

confidence: 99%

“…At finite ℎ 𝑞 , there is some evidence that the critical exponents for 𝑞 = 2, 3, 4 vary with ℎ 𝑞 , i.e. there are second-order phase transitions but they are no longer in the same universality class as the clock models [8][9][10][11][12]. There is also some evidence that these turn into BKT transitions at sufficiently small but positive ℎ 𝑞 [9,13], although there are others who disagree [14,15].…”

Section: Pos(lattice2023)223mentioning

confidence: 99%

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Symmetry Breaking and Clock Model Interpolation in 2D Classical O(2) Spin Systems

Hostetler,

Sakai,

Zhang

et al. 2024

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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Motivated by attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we study an extended-O(2) model that differs from the ordinary O(2) model by the addition of an explicit symmetry breaking term. Its coupling allows to smoothly interpolate between the O(2) model (zero coupling) and a 𝑞-state clock model (infinite coupling). In the latter case, a 𝑞-state clock model can also be defined for noninteger values of 𝑞. Thus, such a limit can also be considered as an analytic continuation of an ordinary 𝑞-state clock model to noninteger 𝑞. In previous work, we established the phase diagram of the model in the infinite coupling limit. We showed that for noninteger 𝑞, there is a second-order phase transition at low temperature and a crossover at high temperature. In this work, we establish the phase diagram at finite values of the coupling using Monte Carlo and tensor methods. We show that for noninteger 𝑞, the second-order phase transition at low temperature and crossover at high temperature persist to finite coupling. For integer 𝑞 = 2, 3, 4, there is a second-order phase transition at infinite coupling (i.e. the clock models). At intermediate coupling, there are second-order phase transitions, but the critical exponents vary with the coupling. At small coupling, the second-order transition for 𝑞 = 4 may turn into a BKT transition.

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Section: Pos(lattice2023)223mentioning

confidence: 99%

Section: Pos(lattice2023)223mentioning

confidence: 99%

Symmetry Breaking and Clock Model Interpolation in 2D Classical O(2) Spin Systems

Hostetler,

Sakai,

Zhang

et al. 2024

Proceedings of the 40th International Symposium on Lattice Field Theory — PoS(LATTICE2023)

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show abstract

Symmetry breaking in an extended O(2) model

Hostetler,

Sakai,

Zhang

et al. 2024

Phys. Rev. D

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Motivated by attempts to quantum simulate lattice models with continuous Abelian symmetries using discrete approximations, we study an extended-O(2) model in two dimensions that differs from the ordinary O(2) model by the addition of an explicit symmetry breaking term −hqcos(qφ). Its coupling hq allows to smoothly interpolate between the O(2) model (hq=0) and a q-state clock model (hq→∞). In the latter case, a q-state clock model can also be defined for noninteger values of q. Thus, such a limit can also be considered as an analytic continuation of an ordinary q-state clock model to noninteger q. In previous work, we established the phase diagram for noninteger q in the infinite coupling limit (hq→∞). We showed that there is a second-order phase transition at low temperature and a crossover at high temperature. In this work, we seek to establish the phase diagram at finite values of the coupling using Monte Carlo and tensor methods. We show that for noninteger q, the second-order phase transition at low temperature and crossover at high temperature persist to finite coupling. For integer q=2, 3, 4, we know there is a second-order phase transition at infinite coupling (i.e. the well-known clock models). At finite coupling, we find that the critical exponents for q=3, 4 vary with the coupling, and for q=4 the transition may turn into a Berezinskii-Kosterlitz-Thouless transition at small coupling. We comment on the similarities and differences of the phase diagrams with those of quantum simulators of the Abelian-Higgs model based on ladder-shaped arrays of Rydberg atoms. Published by the American Physical Society 2024

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Study on the critical properties of thin magnetic films using the clock model

Cited by 2 publications

References 27 publications

Symmetry Breaking and Clock Model Interpolation in 2D Classical O(2) Spin Systems

Symmetry Breaking and Clock Model Interpolation in 2D Classical O(2) Spin Systems

Symmetry breaking in an extended O(2) model

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