Joint min-max distribution and Edwards-Anderson's order parameter of the circular 1/f-noise model
1 LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay - 91405 Orsay, France
2 CNRS-Laboratoire de Physique Théorique de l'École Normale Supérieure - 24 rue Lhomond, 75231 Paris Cedex, France
Received: 20 April 2016
Accepted: 24 May 2016
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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 64.70.Q- – Theory and modeling of the glass transition
© EPLA, 2016