Related papers: Determining Energy Barriers by Iterated Optimizati…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
A novel method for glassy landscape exploration is presented which utilizes a time series of energy values collected during an isothermal relaxation after a thermal quench. A sub-series of increasingly rare events, or quakes, which are…
We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the…
In this paper we try to estimate the lower critical dimension for replica symmetry breaking in spin glasses through the calculation of the additional free-energy required to create a domain wall between two different phases. This mechanism…
According to the mean-field glass theory, the (free) energy landscape of disordered systems is hierarchical and ultrametric if they belong to the full-replica-symmetry-breaking universality class. However, examining this theoretical picture…
We analyse the critical region of finite-($d$)-dimensional Ising spin glass, in particular the limit of $d$ closely above the lower critical dimension $d_\ell$. At criticality the thermally active degrees of freedom are surfaces (of width…
The description of activated relaxation of glassy systems in the multidimensional configurational space is a long-standing open problem. We develop a phenomenological description of the out-of-equilibrium dynamics of a model with a rough…
Spin glasses are frustrated magnetic systems due to a random distribution of ferro- and antiferromagnetic interactions. An experimental three dimensional (3d) spin glass exhibits a second order phase transition to a low temperature spin…
We investigate the nature of the low-energy, large-scale excitations in the three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and free boundary conditions, by studying the response of the ground state to a…
In order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional…
Results are presented for the geometry of low-energy excitations in the one-dimensional Ising spin chain with power-law interactions, in which the model parameters are chosen to yield a finite spin-glass transition temperature. Both…
Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is…
The lower-critical dimension for the existence of the Ising spin-glass phase is calculated, numerically exactly, as $d_L = 2.520$ for a family of hierarchical lattices, from an essentially exact (correlation coefficent $R^2 = 0.999999$)…
The energy of a droplet of linear extent l in the droplet theory of spin glasses goes as l^{\theta} for large l. It is shown by numerical studies of large droplets in two-dimensional systems that this formula needs to be modified by the…
The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of…
A detailed analysis of Monte Carlo data on the two-dimensional Ising spin glass with bimodal interactions shows that the free energy of the model has a nontrivial scaling. In particular, we show by studying the correlation length that much…
We study large-scale, low-energy excitations in the Ising spin glass with Gaussian interactions in two-dimensions at zero temperature, using an optimization algorithm to determine exact ground states. Periodic boundary conditions are…
We present a statistical method for complex energy landscape exploration which provides information on the metastable states--or valleys--actually explored by an unperturbed aging process following a quench. Energy fluctuations of record…
Methods for studying droplets in models with quenched disorder are critically examined. Low energy excitations in two dimensional models are investigated by finding minimal energy interior excitations and by computing the effect of bulk…