Ground-state energy fluctuations in the Sherrington-Kirkpatrick model

The probability distribution function (PDF) of the ground-state energy in the Sherrington-Kirkpatrick spin-glass model is numerically determined by collecting a large statistical sample of ground states, computed using a genetic algorithm. It is shown that the standard deviation of the ground-state energy per spin scales with the number of spins, N, as N^{-\rho} with \rho \simeq 0.765, but the value \rho=3/4 is also compatible with the data, while the previously proposed value \rho=5/6 is ruled out. The PDF satisfies finite-size scaling with a non-Gaussian asymptotic PDF, which can be fitted remarkably well by the Gumbel distribution for the m-th smallest element in a set of random variables, with m \simeq 6.Comment: 4 pages, 4 eps figures. Some changes in the text, references corrected, plot of Tracy-Widom distribution adde

Reply to Comment on "Triviality of the Ground State Structure in Ising Spin Glasses"

We reply to the comment of Marinari and Parisi [cond-mat/0002457 v2] on our paper [Phys. Rev. Lett. 83, 5126 (1999) and cond-mat/9906323]. We show that the data in the comment are affected by strong finite-size corrections. Therefore the original conclusion of our paper still stands.Comment: Reply to comment cond-mat/0002457 on cond-mat/9906323. Final version with minor change

Order-parameter fluctuations in Ising spin glasses at low temperatures

We present a numerical study of the order-parameter fluctuations for Ising spin glasses in three and four dimensions at very low temperatures and without an external field. Accurate measurements of two previously introduced parameters, A and G, show that the order parameter is not self-averaging, consistent with a zero-temperature thermal exponent value \theta' \simeq 0, and confirm the validity of the relation G=1/3 in the thermodynamic limit in the whole low-temperature phase, as predicted by stochastic stability arguments.Comment: 7 pages, 7 eps figures, RevTe

Improving free-energy estimates from unidirectional work measurements: theory and experiment

We derive analytical expressions for the bias of the Jarzynski free-energy estimator from N nonequilibrium work measurements, for a generic work distribution. To achieve this, we map the estimator onto the Random Energy Model in a suitable scaling limit parametrized by (log N)/m, where m measures the width of the lower tail of the work distribution, and then compute the finite-N corrections to this limit with different approaches for different regimes of (log N)/m. We show that these expressions describe accurately the bias for a wide class of work distributions, and exploit them to build an improved free-energy estimator from unidirectional work measurements. We apply the method to optical tweezers unfolding/refolding experiments on DNA hairpins of varying loop size and dissipation, displaying both near-Gaussian and non-Gaussian work distributions.Comment: 4 pages, 3 figure

Comment on ``Triviality of the Ground State Structure in Ising Spin Glasses''

We show that the evidence of cond-mat/9906323 does not discriminate among droplet model and mean field like behavior.Comment: 1 page comment with two .ps figures included. Rewritten version, one error correcte