Second-order phase transition in the fully frustrated<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XY</mml:mi></mml:math>model with next-nearest-neighbor coupling

Chen, Qing-Hu; Luo, Meng-Bo; Jiao, Zhengkuan

doi:10.1103/physrevb.64.212403

Cited by 16 publications

(12 citation statements)

References 27 publications

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“…7 we plot J Rc versus L −11/4 . In analogy with what is observed for the other chiral quantities, the asymptotic behavior sets in only for L ≫ ξ [63]), J ch = 2.212(5) (Ref. [40]), and J ch = 2.203(10) (Ref.…”

Section: Finite-size Scaling At the Chiral Transitionsupporting

confidence: 68%

Multicritical behaviour in the fully frustratedXYmodel and related systems

Pelissetto²,

2005

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Abstract. We study the phase diagram and critical behavior of the two-dimensional square-lattice fully frustrated XY model (FFXY) and of two related models, a lattice discretization of the Landau-Ginzburg-Wilson Hamiltonian for the critical modes of the FFXY model, and a coupled Ising-XY model. We present a finite-size-scaling analysis of the results of high-precision Monte Carlo simulations on square lattices L × L, up to L = O(10 3 ). In the FFXY model and in the other models, when the transitions are continuous, there are two very close but separate transitions. There is an Ising chiral transition characterized by the onset of chiral long-range order while spins remain paramagnetic. Then, as temperature decreases, the systems undergo a Kosterlitz-Thouless spin transition to a phase with quasi-long-range order.The FFXY model and the other models in a rather large parameter region show a crossover behavior at the chiral and spin transitions that is universal to some extent. We conjecture that this universal behavior is due to a multicritical point. The numerical data suggest that the relevant multicritical point is a zero-temperature transition. A possible candidate is the O(4) point that controls the low-temperature behavior of the 4-vector model.Multicritical behavior in the fully frustrated XY model and related systems 2

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Section: Finite-size Scaling At the Chiral Transitionsupporting

confidence: 68%

Multicritical behaviour in the fully frustratedXYmodel and related systems

Pelissetto²,

2005

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“…Several short-time MC simulations were carried out on this model for studying equilibrium phase transitions of the FF JJA model. 5,6,24 The MC method for various current-driven XY models has not been well developed to date, in our opinion. On the other hand, the resistively shunted junction ͑RSJ͒ dynamics has been widely employed to study the dynamics in these models.…”

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confidence: 99%

Nonequilibrium phase transition in fully frustrated Josephson junction arrays: A short-time dynamic approach

2006

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The nonequilibrium phase transition of two-dimensional fully frustrated Josephson junction arrays driven by external currents is studied in the framework of the short-time dynamic scaling approach. Within the resistively shunted junction dynamics, besides the critical temperature T c , the static and dynamic critical exponents 2␤ / , , and z are obtained. The resulting values of T c are consistent with previous steady-state simulations and decrease with the increase of currents. It is found that the values of the exponent are not sensitive to external currents, while the values of 2␤ / and z are strongly current dependent.

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“…The results of numerical studies confirm the existence of two different low-temperature phases, but their accuracy is insufficient for resolving the splitting of both lines of the phase transition into the totally disordered state. A numerical study of the nonlinear relaxation in the same model [174] confirms the presence of a second-order phase transition at x`x 0 and the absence of such a transition at x b x 0 .…”

Section: Structure Of the Phase Diagram With The Next-to-nearest-neigmentioning

confidence: 70%

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Korshunov¹

2006

PHYS-USP

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We discuss the nature and sequence of phase transitions in two-dimensional systems with continuous degeneracy, in which other factors must be taken into account in addition to the interaction of point-like topological excitations, namely, the existence of an additional discrete degeneracy (which leads to the possibility of domain wall formation), the removal of accidental degeneracy by fluctuations, the formation of solitons, and the presence of a random potential acting on vortices. Formally, we discuss various modifications of the two-dimensional XY model, while physical objects that can be described by such models are various arrays of superconducting junctions and noncollinear planar antiferromagnets.

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Second-order phase transition in the fully frustratedXYmodel with next-nearest-neighbor coupling

Cited by 16 publications

References 27 publications

Multicritical behaviour in the fully frustratedXYmodel and related systems

Multicritical behaviour in the fully frustratedXYmodel and related systems

Nonequilibrium phase transition in fully frustrated Josephson junction arrays: A short-time dynamic approach

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