Universal short-time behavior of the dynamic fully frustrated<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>XY</mml:mi></mml:math>model

Luo, H. J.; Schülke, L.; Zheng, Bo

doi:10.1103/physreve.57.1327

Cited by 31 publications

(19 citation statements)

References 30 publications

(31 reference statements)

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“…For example, for the XY model at T = 0.70, t mic ∼ 300 − 400. This increase of t mic for lower temperatures was also noticed in the measurements of the critical initial increase of the magnetization [16,17]. This phenomenon is somehow understandable since at low temperatures the configuration tends to be frozen.…”

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confidence: 69%

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Short-time dynamic behaviour of critical XY systems

Luo¹,

Schulz²,

Schülke³

et al. 1998

Physics Letters A

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Using Monte Carlo methods, the short-time dynamic scaling behaviour of two-dimensional critical XY systems is investigated. Our results for the XY model show that there exists universal scaling behaviour already in the short-time regime, but the values of the dynamic exponent z differ for different initial conditions. For the fully frustrated XY model, power law scaling behaviour is also observed in the short-time regime. However, a violation of the standard scaling relation between the exponents is detected. PACS: 64.60.Ht, 02.70.Lq, 75.10.Hk, 64.60.Fr Keywords: dynamic critical phenomena, Monte Carlo methods, classical spin systemsRecently much progress has been made in critical dynamics. It was discovered that universal scaling behaviour may emerge already in the macroscopic shorttime regime [1,2,3,4,5,6]. Extensive Monte Carlo simulations show that the short-time dynamic scaling is not only conceptually interesting but also practically important, e.g. it leads to new ways for the determination of the critical exponents and the critical temperature [6,7,8,9,10,11,3].For critical systems with second order phase transitions, comprehensive understanding has been achieved. For a relaxational dynamic process of model A starting from an ordered state, the scaling form is given, e.g. for the k-th moment of the magnetization at the critical temperature, by [6,3] where t is the time variable, L is the lattice size, η and z represent the standard static and dynamic critical exponents. This scaling form looks similar to that in the long-time regime but it is now assumed to hold also in the macroscopic short-time regime after a microscopic time scale t mic . For a relaxation process starting from a disordered state with small or zero initial magnetization, the scaling form for the k-th moment at the critical temperature is found to beHere it is important that a new independent critical exponent x 0 has been introduced to describe the dependence of the scaling behaviour on the initial magnetization. The exponent x 0 is the scaling dimension of the global magnetization M(t) and also of the magnetization density. Therefore, even if m 0 = 0, x 0 still enters observables related to the initial conditions. For example, for sufficiently large lattice size the auto-correlation has a power law behaviourwith s i being a spin variable. The exponent λ is related to x 0 by [12]In general, for arbitrary initial magnetization m 0 between 0 and 1 a generalized scaling form can be written down. Renormalization group calculations for the O(N) vector model show that the static exponents η and the dynamic exponent z in the scaling forms (2) and (3) take the same values as in equilibrium or in the long-time regime of the dynamic evolution where they are defined. This is also confirmed by Monte Carlo simulations for various critical magnetic systems with second order phase 1 transitions. Furthermore, numerical results indicate in good accuracy that the values of the exponents η and z are independent of the initial conditions, i.e. ...

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confidence: 69%

“…This scenario is very different from that of critical systems with second order phase transitions. [17], while η and z 1 are from Ref. [17].…”

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confidence: 99%

Short-time dynamic behaviour of critical XY systems

Luo¹,

Schulz²,

Schülke³

et al. 1998

Physics Letters A

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“…problems, including frustrated and/or random systems [19][20][21][22][23]. It has also been extended beyond second-order transitions; e.g., the KT transition [18,[24][25][26][27] and first-order transition systems [28]. In an NER analysis, the equilibration step is not necessary.…”

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confidence: 99%

Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions

et al. 2014

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The critical exponents are estimated for the gauge glass model in two dimensions, in which only the Kosterlitz-Thouless (KT) phase appears in the low-temperature regime. The nonequilibrium relaxation method is applied to estimate the transition temperature and critical exponents: the static exponent η and the dynamical exponent z. Since the system exhibits criticality in the whole KT phase, we estimate the exponents on the boundary as well as inside the KT phase. The static exponent η depends on both the temperature and the strength of randomness, while the dynamical one z is almost constant throughout the KT phase, including the boundary.

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“…Extensive Monte Carlo ͑MC͒ simulations showed that the short-time dynamic scaling is not only conceptually interesting but also practically important, e.g., it leads to new ways for the determination of the critical exponents and the critical temperature. 20,21 Recently, Franzese et al 22 have studied the phase transitions of the 2D FFXY model on a square lattice with nearest neighbor ͑NN͒ and next-nearest neighbor ͑NNN͒ couplings by analyzing Binder's cumulant of magnetization up to system size Lϭ72. They found that an Ising-like transition and a KT transition coexist when xϽx c ϭ1/ͱ2 and the critical temperatures T c Z 2 and T c U(1) decrease with increasing x, where x is the ratio between NNN and NN couplings.…”

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confidence: 99%

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

2001

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The short time dynamic behavior of the second-order phase transition in the two-dimensional fully frustrated XY model with nearest-neighbor ͑NN͒ and next-nearest-neighbor ͑NNN͒ couplings is investigated using Monte Carlo simulations. When xϽ1/ͱ2 (x is the ratio between NNN and NN couplings͒, the transition temperature T c and the dynamic and static critical exponents z, 2␤/, and are estimated using the short-time dynamic scaling analysis. Except x close to the critical value 1/ͱ2, the critical exponents 2␤/ and are found to be almost independent of the NNN coupling, indicating that the second-order phase transitions in the FFXY model, with or without NNN coupling, are in the same universality class. When xϾ1/ͱ2, the short-time dynamic study suggests that there is no second-order phase transition, in agreement with the previous result ͓Phys. Rev. B 62, R9287 ͑2000͔͒.

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Universal short-time behavior of the dynamic fully frustratedXYmodel

Cited by 31 publications

References 30 publications

Short-time dynamic behaviour of critical XY systems

Short-time dynamic behaviour of critical XY systems

Numerical studies on critical properties of the Kosterlitz-Thouless phase for the gauge glass model in two dimensions

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

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