arXiv subjects
Publications and source records attributed to Matteo Palassini.
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.
The nature of the spin glass state is investigated by studying changes to the ground state when a weak perturbation is applied to the bulk of the system. We consider short range models in three and four dimensions and the infinite range Sherrington-Kirkpatrick (SK) and Viana-Bray models. Our results for the SK and Viana-Bray models agree with the replica symmetry breaking picture. The data for the short range models fit naturally a picture in which there are large scale excitations which cost a finite energy but whose surface has a fractal dimension, $d_s$, less than the space dimension $d$. We also discuss a possible crossover to other behavior at larger length scales than the sizes studied.
We investigate the ground state structure of the three-dimensional Ising spin glass in zero field by determining how the ground state changes in a fixed finite block far from the boundaries when the boundary conditions are changed. We find that the probability of a change in the block ground state configuration tends to zero as the system size tends to infinity. This indicates a trivial ground state structure, as predicted by the droplet theory. Similar results are also obtained in two dimensions.
We study the 3D Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Using an iterative extrapolation procedure, Monte Carlo data are extrapolated to infinite volume up to correlation length ξ= 140. The infinite volume data are consistent with both a continuous phase transition at finite temperature and an essential singularity at finite temperature. An essential singularity at zero temperature is excluded.
We investigate the ground state structure of Ising spin glasses in zero magnetic field by determining how the ground state changes in a fixed finite block far from the boundaries when the boundary conditions are changed. We find, both in two and three dimensions, that the probability of a change in the block ground state configuration tends to zero as the system size tends to infinity. This indicates a trivial ground state structure, as predicted by the droplet theory.
We study how the ground state of the two-dimensional Ising spin glass with Gaussian interactions in zero magnetic field changes on altering the boundary conditions. The probability that relative spin orientations change in a region far from the boundary goes to zero with the (linear) size of the system L like L^{-lambda}, where lambda = -0.70 +/- 0.08. We argue that lambda is equal to d-d_f where d (=2) is the dimension of the system and d_f is the fractal dimension of a domain wall induced by changes in the boundary conditions. Our value for d_f is consistent with earlier estimates. These results show that, at zero temperature, there is only a single pure state (plus the state with all spins flipped) in agreement with the predictions of the droplet model.
We study the three-dimensional Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Monte Carlo data are extrapolated to infinite volume with an iterative procedure up to correlation lengths xi \approx 140. The infinite volume data are consistent with a conventional power law singularity at finite temperature Tc. Taking into account corrections to scaling, we find Tc = 1.156 +/- 0.015, nu = 1.8 +/- 0.2 and eta = -0.26 +/- 0.04. The data are also consistent with an exponential singularity at finite Tc, but not with an exponential singularity at zero temperature.
We compute the effect of small-size instantons on the coefficient function of the chiral condensate in the operator product expansion of current-current correlators. Furthermore, we also compute the instanton corrections associated with four-quark and six-quark operators in the factorization approximation. We discuss the phenomenological implications of our result.