Nonequilibrium relaxation analysis of Kosterlitz-Thouless phase transition

Ozeki, Yukiyasu; Ogawa, Keita; Ito, Nobuyasu

doi:10.1103/physreve.67.026702

Cited by 42 publications

(47 citation statements)

References 28 publications

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“…From scaling analyses based on the dynamic scaling hypothesis, we obtained i = 0.901͑1͒ and m = 0.910͑1͒. Ozeki et al [18] proposed a more efficient method of determining the critical point of the KT transition. In their method, relative values of the relaxation times are estimated by scaling.…”

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confidence: 98%

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Critical exponents of isotropic-hexatic phase transition in the hard-disk system

2004

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The hard-disk system is studied by observing the nonequilibrium relaxation behavior of a bond-orientational order parameter. The density dependence of characteristic relaxation time tau is estimated from the finite-time scaling analysis. The critical point between the fluid and the hexatic phase is refined to be 0.899 (1) by assuming the divergence behavior of the Kosterlitz-Thouless transition. The value of the critical exponent eta is also studied by analyzing the fluctuation of the order parameter at the criticality and estimated as eta=0.25 (2). These results are consistent with the prediction by the Kosterlitz-Thouless-Halperin-Nelson-Young theory.

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confidence: 98%

“…This analysis is called the nonequilibrium relaxation (NER) method. This method has been used to study phase diagrams and to determine accurate values of critical points and critical exponents for transitions of various systems: spin-glass transition [15], chiral-glass transition [16], and the KT transition [17,18].…”

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confidence: 99%

Critical exponents of isotropic-hexatic phase transition in the hard-disk system

2004

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“…This method is called a NER method. Watanabe et al [10,11] studied two-dimensional melting based on the NER method for the Kosterlitz-Thouless transition [25] by observing the relaxation behavior of φ 6 . Therefore, the following time evolutions of φ 6 contains information about the twodimensional melting transition.…”

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confidence: 99%

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

2006

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We construct a rejection-free Monte Carlo method for the hard-disk system. Rejection-free Monte Carlo methods preserve the time-evolution behavior of the standard Monte Carlo method, and this relationship is confirmed for our method by observing nonequilibrium relaxation of a bondorientational order parameter. The rejection-free method gives a greater computational efficiency than the standard method at high densities. The rejection free method is implemented in a shrewd manner using optimization methods to calculate a rejection probability and to update the system. This method should allow an efficient study of the dynamics of two-dimensional solids at high density.

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“…It pro-vides the critical temperature and critical exponents accurately for second-order transition systems, [29][30][31] and has been used successfully to study various problems, including frustrated and/or random systems. 32 It has also been extended beyond second-order transitions; e.g., the KT transition 31,33,34 and the first-order transition systems. 35 In the NER analysis, the equilibration step is not necessary.…”

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“…͑3͒, with 0 ഛ A ij ഛ 2. For both types of models, the parameter D controls the randomness, and the KT phase is observed in the pure case ͑D = ϱ͒; the transition temperature for the pure case has been estimated numerically as T KT 0 ϳ 0.894 for the cosine-type 34 and T KT 0 ϳ 1.33 for the Villain-type. 37 The temperature is measured in a unit of J / k B in the following.…”

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Nonequilibrium relaxation analysis of gauge glass models in two dimensions

Ozeki

Ogawa

2005

Phys. Rev. B

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The Kosterlitz-Thouless ͑KT͒ transition is investigated for gauge glass models in two dimensions by means of the nonequilibrium relaxation ͑NER͒ method. Two kinds of models, which have the same symmetry, are analyzed. Using the scaling analysis of the NER function on a large lattice with L = 1000, we confirm the KT transition numerically for both models. This indicates the stability of the KT phase against a small disorder, which was previously claimed by perturbation expansion and renormalization group arguments.The gauge glass ͑GG͒ model is a classical spin system with quenched disorder and has attracted much attention. It describes the thermodynamics of various systems such as disordered magnets with random Dzyaloshinskii-Moriya interaction, 1 Josephson-junction arrays with positional disorder in a magnetic field, 2 vortex glasses, 3 and crystal systems on disordered substrates. 4 In three dimensions, the spin-glass ͑SG͒ transition for a strongly disordered regime has been confirmed in the GG systems theoretically, 5,6 as well as experimentally. 7 In two dimensions, there is a controversy about the existence of the SG-like phase in the strongly disordered regime. Some numerical simulations suggested the quasi-long-range order, 8,9 while experimental observation 10 and other numerical simulations 6,11-14 deny it. Although the long-range SG order is denied in two dimensions following the Marmine-type argument, 15 there is a possibility of a phase in which the SG correlation decays in a power law. 16 In weakly disordered regime, there has been another controversy about the existence of the reentrant transition from the Kosterlitz-Thouless ͑KT͒ phase 17 to the non-KT one. Earlier works with real-space renormalization group ͑RG͒ analysis suggest reentrance. 1,2,18,19 The analysis has been modified and provides the absence of it. [20][21][22] The same results are obtained by Monte Carlo simulations. 4,6,9,13,23,24 and the RG analyses. 20,25 With all these studies, the instability of the KT phase against a small disorder is pointed out by the perturbation expansion and the RG analysis. 26,27 However, it is denied by numerical simulations 4,6,9,13 and other RG analyses. 9,20-22 Analytically, the gauge theory, which has provided several exact relations in Ising SG models, shows the absence of reentrance if the KT phase appears in a finite disordered regime. 16 The same result is also derived from a dynamical point of view obtained by the dynamical gauge theory. 28 While the results of gauge theory are plausible, it is necessary to assume the stability of the KT phase. Investigation of the phase diagram of these random XY models is still at a primitive stage as compared to the case of the Ising model.In the present study, we apply the nonequilibrium relaxation ͑NER͒ analysis to the GG models in two dimensions in order to clarify the stability of the KT phase against a small disorder. The NER method has been an efficient numerical technique for analyzing equilibrium phase transitions. It pro-vides the critical temperatu...

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Nonequilibrium relaxation analysis of Kosterlitz-Thouless phase transition

Cited by 42 publications

References 28 publications

Critical exponents of isotropic-hexatic phase transition in the hard-disk system

Critical exponents of isotropic-hexatic phase transition in the hard-disk system

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems

Nonequilibrium relaxation analysis of gauge glass models in two dimensions

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