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arXiv · 1604.02282

Joint min-max distribution and Edwards-Anderson's order parameter of the circular $1 / f$-noise model

Xiangyu Cao·Pierre Le Doussal
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Abstract

We calculate the joint min--max distribution and the Edwards-Anderson's order parameter for the circular model of $1 / f$-noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial techniques. Numerical checks come with significantly improved control of finite-size effects in the glassy phase, and the results convincingly validate the freezing-duality conjecture. Application to diffusive dynamics is discussed. We also provide a formula for the pre-factor ratio of the joint/marginal Carpentier-Le Doussal tail for minimum/maximum which applies to any logarithmic random energy model.

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Xiangyu Cao, Pierre Le Doussal. 2016-04-08. Joint min-max distribution and Edwards-Anderson's order parameter of the circular $1 / f$-noise model. https://doi.org/10.1209/0295-5075%2F114%2F40003

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