Statistics of lowest droplets in two-dimensional Gaussian Ising spin glasses

22 pages, REVTeX, 13 figuresInternational audienceA new approach to determine the value of the zero-temperature thermalexponent theta in spin glasses is presented. It consists in describingthe energy level spectrum in spin glasses only in terms of theproperties of the lowest energy droplets and the lowest dropletexponents (LDEs) lambda_l,theta_l that describe the statistics oftheir sizes and gaps. We show how these LDEs yield the standardthermal exponent of droplet theory theta through the relation,theta=theta_l+d*lambda_l. The present approach provides a new way tomeasure the thermal exponent theta without any assumption about thecorrect procedure to generate typical low-lying excitations as iscommonly done in many perturbation methods including domain wallcalculations. To illustrate the usefulness of the method we present adetailed investigation of the properties of the lowest energy dropletsin two-dimensional Gaussian Ising spin glasses. By independentmeasurements of both LDEs and an aspect-ratio analysis, we findtheta(2d)~-0.46(1)< theta_{DW}(2d)~-0.287 where theta_{DW} is thethermal exponent obtained in domain-wall theory. We also discuss theorigin of finite-volume corrections in the behavior of the LDE theta_land relate them to the finite-volume corrections in the statistics ofextreme values. All in all, we show that typical large-scale dropletsare not probed by most of the present perturbation methods as theyprobably do not have a compact structure as has been recentlysuggested