Joint min-max distribution and Edwards-Anderson's order parameter of the circular 1/f-noise model. (13th June 2016) - Cao, Xiangyu; Le Doussal, Pierre
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.