Disorder-Induced Phase Transitions in Two-Dimensional Crystals

Cha, Min-Chul; Fertig, H. A.

doi:10.1103/physrevlett.74.4867

Cited by 88 publications

(109 citation statements)

References 15 publications

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“…In 2D, our simulations imply that weak disorder is marginal 19,20,21,22 and a system with strong disorder flows to a disordered fixed point. There is no sign of a re-entrant transition in our simulations.…”

Section: Discussion and Summarymentioning

confidence: 99%

“…Studies in 2D 16,17,18 suggest that weak disorder (α 0) does not affect the existence of an ordered phase at intermediate temperature but there is a re-entrant transition to a disordered phase at low temperature. However, recent analytic 19,20,21,22 and numerical 8 studies show there is an ordered phase for T < T c (α) with T c (α) > 0 for 0 ≤ α < α c . To study how the disorder strength behaves as the length scale L varies, one must, if possible, identify the scaled disorder strength A(L) with some measurable quantity.…”

Section: Varying Disorder Strength In 2d and 3dmentioning

confidence: 99%

“…17,18 These studies 16,17,18 showed that the existence of weak disorder (α ≪ 1) does not destroy an ordered phase at intermediate temperature but predict a re-entrant transition to a disordered phase at low temperature in two dimensions. However, recent analytic 19,20,21,22 and numerical 8 studies suggest the absence of a re-entrant transition and that there exists an ordered phase for T < T c (α) when α < α c .…”

Section: Introductionmentioning

confidence: 99%

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Domain wall renormalization group study of theXYmodel with quenched random phase shifts

Akino

Kosterlitz

2002

Phys. Rev. B

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The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations yield spin stiffness exponents θs ≈ −0.36 in 2D and θs ≈ +0.31 in 3D, which are considerably larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the ±J XY spin glass in 3D, we obtain a spin stiffness exponent θs ≈ +0.10 which supports the existence of spin glass order at finite temperature in contrast with previous estimates which obtain θs < 0. Our method also allows us to study renormalization group flows of both the coupling constant and the disorder strength with length scale L. Our results are consistent with recent analytic and numerical studies suggesting the absence of a re-entrant transition in 2D at low temperature. Some possible consequences and connections with real vortex systems are discussed.

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Section: Discussion and Summarymentioning

confidence: 99%

Section: Varying Disorder Strength In 2d and 3dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Domain wall renormalization group study of theXYmodel with quenched random phase shifts

Akino

Kosterlitz

2002

Phys. Rev. B

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“…The case (1.2) corresponds to a situation where the average magnetic flux over each elementary plaquette of the grain network is an integer multiple of Φ 0 , but random displacement of superconducting grains from a perfect lattice structure yields quenched random phase shifts [7,11]. On the theoretical side, model (1.1) and its variants have been studied extensively in the past [5,[12][13][14][15][16][17][18][19]. Result of previous studies can be summarized as follows.…”

Section: Introductionmentioning

confidence: 99%

Vortex statistics in a disordered two-dimensionalXYmodel

Tang

1996

Phys. Rev. B

109

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The equilibrium behavior of vortices in the classical two-dimensional (2D) XY model with uncorrelated random phase shifts is investigated. The model describes Josephson-Junction arrays with positional disorder, and has ramifications in a number of other bond-disordered 2D systems. The vortex Hamiltonian is that of a Coulomb gas in a background of quenched random dipoles, which is capable of forming either a dielectric insulator or a plasma. We confirm a recent suggestion by Nattermann, Scheidl, Korshunov, and Li [J. Phys. I (France) 5, 565 (1995)], and by Cha and Fertig [Phys. Rev. Lett. 74, 4867 (1995)] that, when the variance σ of random phase shifts is smaller than a critical value σc, the system is in a phase with quasi-long-range order at low temperatures, without a reentrance transition. This conclusion is reached through a nearly exact calculation of the single-vortex free energy, and a Kosterlitz-type renormalization group analysis of screening and random polarization effects from vortex-antivortex pairs. The critical strength of disorder σc is found not to be universal, but generally lies in the range 0 < σc < π/8. Argument is presented to suggest that the system at σ > σc does not possess long-range glassy order at any finite temperature. In the ordered phase, vortex pairs undergo a series of spatial and angular localization processes as the temperature is lowered. This behavior, which is common to many glass-forming systems, can be quantified through approximate mappings to the random energy model and to the directed polymer on the Cayley tree. Various critical properties at the order-disorder transition are calculated.75.10. Nr, 64.60.Ak, 74.50.+r, 74.60.Ge

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“…237,238,239,240,241 Here we follow the heuristic argument given by the authors of [238]. They argued that there is a disorder induced phase transition at zero temperature in the twodimensional XY model.…”

Section: Phase Diagram Of the Random Xy Model In Two Dimensionsmentioning

confidence: 99%

Recent Progress in Spin Glasses

Kawashima

Rieger

2013

Frustrated Spin Systems

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We review recent findings on spin glass models. Both the equilibrium properties and the dynamic properties are covered. We focus on progress in theoretical, in particular numerical, studies, while its relationship to real magnetic materials is also mentioned.The motivation that pulls researchers toward spin glasses is possibly not the potential future use of spin glass materials in "practical" applications. It is rather the expectation that there must be something very fundamental in systems with randomness and frustration. It seems that this expectation has been acquiring a firmer ground as the difficulty of the problem is appreciated more clearly. For example, a close relationship has been established between spin glass problems and a class of optimization problems known to be N P -hard. It is now widely accepted that a good (i.e. polynomial) computational algorithm for solving any one of N P -hard problems most probably does not exist. Therefore, it is quite natural to expect that the Ising spin glass problem, as one of the problem in the class, would be very hard to solve, which indeed turns out to be the case in a vast number of numerical studies. None the less, it is often the case that only numerical studies can decide whether a certain hypothetical picture applies to a given instance. Consequently, the major part of what we present below is inevitably a de-

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Disorder-Induced Phase Transitions in Two-Dimensional Crystals

Cited by 88 publications

References 15 publications

Domain wall renormalization group study of theXYmodel with quenched random phase shifts

Domain wall renormalization group study of theXYmodel with quenched random phase shifts

Vortex statistics in a disordered two-dimensionalXYmodel

Recent Progress in Spin Glasses

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