Rounding of first-order phase transitions in systems with quenched disorder

Aizenman, Michael; Wehr, Jan

doi:10.1103/physrevlett.62.2503

Cited by 600 publications

(671 citation statements)

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“…10 a). This may be analogous in the time domain, to the phenomenon observed in phase transitions, where it has been shown that microscopic random impurities or other type of spatial disorder, may produce rounding of a first-order phase transition [31][32][33][34]. If the most probable value of the PDF is taken as an order parameter, the transition obviously remains discontinuous but the bistability range is modified by noise (Fig.…”

Section: Experimental Results For the Electronic Circuitmentioning

confidence: 99%

Effect of multiplicative noise on parametric instabilities

Berthet¹,

Petrossian

Residori

et al. 2003

Physica D: Nonlinear Phenomena

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We report a study on the effect of external multiplicative noise on parametric instabilities using two different experimental systems: an electronic RLC circuit, parametrically pumped with a voltage-variable capacitor, and surface waves generated by vertically vibrating a layer of fluid (the Faraday instability). Both systems are forced by the superposition of a sinusoidal and a noisy component. We study the statistical properties of the response of both systems to noisy parametric forcing and compare them with theoretical predictions. When the detuning from parametric resonance is such that the bifurcation in the absence of noise is supercritical, both systems behave in the same way under the influence of noise. We find that the effect of noise is twofold: on one hand, it triggers the instability before its deterministic onset under the form of oscillatory bursts; on the other hand, it inhibits the nonlinearly saturated oscillatory response above the deterministic onset. When the detuning is such that the bifurcation is subcritical, we find that the two systems behave differently. In the case of the electronic oscillator, noise mostly triggers random transitions between the two states of the bistable region that exists in the absence of noise, whereas in the surface wave experiment new states are created by noise and the bistable region is strongly enlarged.

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Section: Experimental Results For the Electronic Circuitmentioning

confidence: 99%

Effect of multiplicative noise on parametric instabilities

Berthet¹,

Petrossian

Residori

et al. 2003

Physica D: Nonlinear Phenomena

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“…The calculations for the Potts model with random dilution that have previously been performed in two dimensons [17][18][19] show that critical behaviour in the second order regime is the same as that of the Ising model. Our preliminary results for the specific heat support the thesis that this might be also true in the aerogel case in three dimensions, but more funded calculations are needed.…”

Section: Discussionmentioning

confidence: 99%

“…Previous studies of the two dimensional Potts model in a randomly diluted medium [17][18][19] show crossover from first order to second order type behaviour. The same effect was also discussed in more a general context by Berker [20].…”

Section: Introductionmentioning

confidence: 99%

Numerical study of phase transitions inside the pores of aerogels

Uzelac

Hasmy²,

Jullien³

1995

Journal of Non-Crystalline Solids

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Phase transitions inside the pores of an aerogel are investigated by modelizing the aerogel structure by diffusion-limited cluster-cluster aggregation on a cubic lattice in a finite box and considering q-states Potts variables on the empty sites interacting via nearest-neighbours. Using a finite size scaling analysing of Monte-Carlo numerical results, it is concluded that for q = 4 the transition changes from first order to second order as the aerogel concentration (density) increases. Comparison is made with the case q = 3 (where the first order transition is weaker in three dimensions) and with the case q = 4 but for randomly (non correlated) occupied sites. Possible applications to experiments are discussed.PACS numbers: 64.60-Ak, 05.50-Fh, 75.40-Mg Typeset using REVT E X * a short report of this work has been published in Phys. Rev. Lett. 74, 422 (1995).

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“…Imbrie (1984) showed that if the disorder is small, the model in dimension ¿ exhibits long-range order at zero temperature. Aizenmann and Wehr (1989) …”

Section: Equilibrium Properties Of Random Field Ising Modelmentioning

confidence: 99%