Nonequilibrium relaxation analysis of fully frustrated<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XY</mml:mi></mml:math>models in two dimensions

Ozeki, Yukiyasu; Ito, Nobuyasu

doi:10.1103/physrevb.68.054414

Cited by 63 publications

(70 citation statements)

References 41 publications

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“…Noh et al also postulated that only for large enough system the Ising-like behavior is observed. However, using nonequilibrium relaxation study for large enough systems up to L = 2000, Ozeki and Ito [11] recently obtained the ν = 0.83 (2), which suggests that the corrections to FSS are not so serious. Thus, more careful calculations will be needed for the critical phenomena of chiral transition.…”

Section: Chiral Phase Transitionmentioning

confidence: 99%

“…The so-called two-dimensional (2D) fully frustrated XY models have attracted an extensive investigation in the last two decades [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. Due to the frustration the systems possess additional discrete reflection symmetry Z 2 , apart from the global spin rotation symmetry U (1).…”

Section: Introductionmentioning

confidence: 99%

“…As a 2D frustrated XY system, two lattice systems are frequently studied numerically. The first one is the square lattice where the interactions can be a regular mixture of ferromagnetic (F) and antiferromagnetic (AF) couplings (Villain model) [1,2,3,4,5,6,7,8,9,10,11,15]. The second one is the AF XY model on the triangular lattice [2,4,8,11,12,13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

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Study of the fully frustrated clock model using the Wang–Landau algorithm

Surungan

Okabe

Tomita

2004

J. Phys. A: Math. Gen.

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Monte Carlo simulations using the newly proposed Wang-Landau algorithm together with the broad histogram relation are performed to study the antiferromagnetic six-state clock model on the triangular lattice, which is fully frustrated. We confirm the existence of the magnetic ordering belonging to the Kosterlitz-Thouless (KT) type phase transition followed by the chiral ordering which occurs at slightly higher temperature. We also observe the lower temperature phase transition of KT type due to the discrete symmetry of the clock model. By using finite-size scaling analysis, the higher KT temperature T2 and the chiral critical temperature Tc are respectively estimated as T2 = 0.5154(8) and Tc = 0.5194(4). The results are in favor of the double transition scenario. The lower KT temperature is estimated as T1 = 0.496(2). Two decay exponents of KT transitions corresponding to higher and lower temperatures are respectively estimated as η2 = 0.25(1) and η1 = 0.13(1), which suggests that the exponents associated with the KT transitions are universal even for the frustrated model.

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Section: Chiral Phase Transitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Study of the fully frustrated clock model using the Wang–Landau algorithm

Surungan

Okabe

Tomita

2004

J. Phys. A: Math. Gen.

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“…Matsubara et al 15,16,17 showed several lines of evidence that the spin-glass transition occurs at a finite temperature. Nakamura et al 18,19 investigated the model by a nonequilibrium relaxation method 20,21,22,23,24 and obtained the consistent results. Here, we note that nonequilibrium relaxation of the spinglass susceptibility 25 and that of the Binder parameter 26 are known to exhibit the algebraic divergence at the spinglass transition temperature in the Ising model.…”

Section: Introductionmentioning

confidence: 87%

“…The second method to estimate the transition temperature is the finite-time scaling analysis 23 . This is a direct interpretation of the conventional finite-size scaling analysis by considering the dynamic scaling hypothesis: τ ∼ ξ z .…”

Section: B Nonequilibrium Relaxation Methodsmentioning

confidence: 99%

Nonvanishing spin-glass transition temperature of the±JXYmodel in three dimensions

2004

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A three-dimensional ±J XY spin-glass model is investigated by a nonequilibrium relaxation method. We have introduced a new criterion for the finite-time scaling analysis. A transition temperature is obtained by a crossing point of obtained data. The scaling analysis on the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility shows that both transitions occur simultaneously. The result is checked by relaxation functions of the Binder parameters and the glass correlation lengths of the spin and the chirality. Every result is consistent if we consider that the transition is driven by the spin degrees of freedom.

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Nonequilibrium relaxation method — an alternative simulation strategy

Ito

2005

Pramana - J Phys

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Nonequilibrium relaxation analysis of fully frustratedXYmodels in two dimensions

Cited by 63 publications

References 41 publications

Study of the fully frustrated clock model using the Wang–Landau algorithm

Study of the fully frustrated clock model using the Wang–Landau algorithm

Nonvanishing spin-glass transition temperature of the±JXYmodel in three dimensions

Nonequilibrium relaxation method — an alternative simulation strategy

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