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

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.

6 pages, 3 figures

References in corpus (4)

• Extremes of the discrete two-dimensional Gaussian free field
• Spatial Extent of Branching Brownian Motion
• High values of disorder-generated multifractals and logarithmically correlated processes
• Statistics of Fluctuating Colloidal Fluid-Fluid Interfaces

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• Disordered statistical physics in low dimensions: extremes, glass transition, and localization