Equilibriumlike invaded cluster algorithm: Critical exponents and dynamical properties

Balog, Ivan; Uzelac, Katarina

doi:10.1103/physreve.81.041111

Cited by 3 publications

(7 citation statements)

References 32 publications

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“…In our previous works [29,34], we have shown that introducing auxiliary parameters, which constrain the resulting distribution of bond probability p to the width narrower than L − d 2 , reestablishes the sampling of the canonical ensemble. Such a modified algorithm thus produces the equilibrium configurations at the quasicritical point of the finite system.…”

Section: A Eic Approachmentioning

confidence: 98%

“…We have chosen the set of auxiliary parameters of the EIC algorithm [29,34] to be v = 1 10 L −1.1 and N a = 1000. The values of [p 2 α − p 2 α ] (Fig.…”

Section: A Details Of the Simulationmentioning

confidence: 99%

“…In Sec. II we define the model which we study and describe the "equilibrium-like invaded cluster" algorithm [29,34] and its application in the presence of bond disorder. In Sec.…”

Section: Introductionmentioning

confidence: 99%

“…[34]), i.e., that the fluctuations in a bond variable scale with power law dependence narrower than L − d . 7.…”

mentioning

confidence: 99%

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Quenched disorder: Demixing thermal and disorder fluctuations

Balog

Uzelac

2012

Phys. Rev. E

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We present a finite-size scaling study of the phase transition in the two-dimensional Potts model modified by random bond disorder, in which the average is taken over quantities calculated at quasicritical temperatures of individual disorder configurations. We used the recently proposed equilibrium-like invaded cluster algorithm, which allows us to examine separately the fluctuations in the thermodynamical ensemble from the fluctuations induced by changing the disorder configuration. We point out the crucial role of the spatial inhomogeneities on all scales for the critical behavior of the system. These inhomogeneities are formed by "dressing" of the disorder via critical correlations and are demonstrated to exist for any system size despite the critical fluctuations in thermodynamical ensemble. Such inhomogeneities were previously not thought to be relevant in disorder-altered classical systems when critical temperature is finite. However, we confirm that only by averaging at quasicritical temperatures of each disorder configuration is the thermal critical exponent y(τ) not obscured by the influence of the aforementioned spatial inhomogeneities.

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Section: A Eic Approachmentioning

confidence: 98%

“…We have chosen the set of auxiliary parameters of the EIC algorithm [29,34] to be v = 1 10 L −1.1 and N a = 1000. The values of [p 2 α − p 2 α ] (Fig.…”

Section: A Details Of the Simulationmentioning

confidence: 99%

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Quenched disorder: Demixing thermal and disorder fluctuations

Balog

Uzelac

2012

Phys. Rev. E

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“…Recent efforts on the theoretical and numerical studies can be found for example in Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. It has been rigorously proven that an infinitesimal amount of quenched disorder coupled to the energy density will turn a first-order transition to a continuous one when the spatial dimension d 2 [17,18].…”

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Corrections to scaling in the dynamic approach to the phase transition with quenched disorder

Wang¹,

Zhou²,

Zheng³

2014

EPL

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-With dynamic Monte Carlo simulations, we investigate the continuous phase transition in the three-dimensional three-state random-bond Potts model. We propose a useful technique to deal with the strong corrections to the dynamic scaling form. The critical point, static exponents β and ν, and dynamic exponent z are accurately determined. Particularly, the results support that the exponent ν satisfies the lower bound ν 2/d.Introduction. -The effects of quenched disorder on phase transitions are of great interest in physics for decades. Recent efforts on the theoretical and numerical studies can be found for example in Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. It has been rigorously proven that an infinitesimal amount of quenched disorder coupled to the energy density will turn a first-order transition to a continuous one when the spatial dimension d 2 [17,18]. This phenomenon has been observed, for example, in the two-dimensional (2D) eight-state Potts model, Blume-Capel model and three-Color Ashkin-Teller model [13,19,20]. For the case of d = 3, the phase transition may persist first order if the strength of quenched disorder is weak, and then soften to continuous if the strength is strong enough [10,14,21,22].The effects of quenched disorder, imposed to a pure system with a continuous phase transition, can be judged by the specific heat exponent α p or the correlation length exponent ν p of the pure system according to the Harris criterion [23]. If α p < 0 or ν p > 2/d, the disorder is irrelevant to the critical behavior, and if α p > 0 or ν p < 2/d, the disorder is relevant, and leads to a new universality class governed by the 'disorder' fixed point [7,11]. For the marginal case α p = 0, the criterion can not give a conclusion whether the disorder is relevant or not, and numerical results support that the model obeys the strong universality hypothesis with logarithmic correlations [5,24]. On the other hand, for a disordered system with a continuous phase transition, which is governed by the 'disorder' fixed point, the specific heat exponent α does not decide whether the disorder is relevant. It is only proven that a lower bound ν 2/d should be satisfied [25][26][27].To clarify the effects of quenched disorder on phase transitions, extensive numerical studies have been performed, for example, for the three-dimensional (3D) q-state site-diluted Potts model, bond-diluted Potts model and random-bond Potts model [4,12,15,16,22]. Recently, a numerical study based on the finite-time scaling and dynamic Monte Carlo renormalization-group methods gives ν = 0.554(9) for the 3D three-state random-bond

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Inhomogeneities on all scales at a phase transition altered by disorder

Balog

Uzelac

2012

Phys. Rev. E

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We have done a finite-size scaling study of a continuous phase transition altered by the quenched bond disorder, investigating systems at quasicritical temperatures of each disorder realization by using the equilibriumlike invaded cluster algorithm. Our results indicate that in order to access the thermal critical exponent y τ , it is necessary to average the free energy at quasicritical temperatures of each disorder configuration. Despite the thermal fluctuations on the scale of the system at the transition point, we find that spatial inhomogeneities form in the system and become more pronounced as the size of the system increases. This leads to different exponents describing rescaling of the fluctuations of observables in disorder and thermodynamic ensembles. An important aspect present in the majority of the cited problems is the non-selfaveraging effect between different disorder realizations [7], leading to the question of proper averaging over disorder. The standard approach is to reduce the problem to an effective translationally invariant one, by averaging the free energy over disorder configurations at

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Equilibriumlike invaded cluster algorithm: Critical exponents and dynamical properties

Cited by 3 publications

References 32 publications

Quenched disorder: Demixing thermal and disorder fluctuations

Quenched disorder: Demixing thermal and disorder fluctuations

Corrections to scaling in the dynamic approach to the phase transition with quenched disorder

Inhomogeneities on all scales at a phase transition altered by disorder

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