Zero-temperature responses of a 3D spin glass in a field

We probe the energy landscape of the 3D Edwards-Anderson spin glass in a magnetic field to test for a spin glass ordering. We find that the spin glass susceptibility is anomalously large on the lattice sizes we can reach. Our data suggest that a transition from the spin glass to the paramagnetic phase takes place at B_c=0.65, though the possibility B_c=0 cannot be excluded. We also discuss the question of the nature of the putative frozen phase.Comment: RevTex, 4 pages, 4 figures, clarifications and added reference

Spin and link overlaps in 3-dimensional spin glasses

Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean field picture of a non-trivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically non-trivial and they reach out to the boundaries of the lattice. Their surface to volume ratios decrease as L increases and may asymptotically go to zero. If so, link and window overlaps between the ground state and these excited states become ``trivial''.Comment: Extra fits comparing TNT to mean field, summarized in a tabl

Deviations from the mean field predictions for the phase behaviour of random copolymers melts

We investigate the phase behaviour of random copolymers melts via large scale Monte Carlo simulations. We observe macrophase separation into A and B--rich phases as predicted by mean field theory only for systems with a very large correlation lambda of blocks along the polymer chains, far away from the Lifshitz point. For smaller values of lambda, we find that a locally segregated, disordered microemulsion--like structure gradually forms as the temperature decreases. As we increase the number of blocks in the polymers, the region of macrophase separation further shrinks. The results of our Monte Carlo simulation are in agreement with a Ginzburg criterium, which suggests that mean field theory becomes worse as the number of blocks in polymers increases.Comment: 6 pages, 4 figures, Late

Ground-State Properties of a Heisenberg Spin Glass Model with a Hybrid Genetic Algorithm

We developed a genetic algorithm (GA) in the Heisenberg model that combines a triadic crossover and a parameter-free genetic algorithm. Using the algorithm, we examined the ground-state stiffness of the $\pm J$ Heisenberg model in three dimensions up to a moderate size range. Results showed the stiffness constant of $\theta = 0$ in the periodic-antiperiodic boundary condition method and that of $\theta \sim 0.62$ in the open-boundary-twist method. We considered the origin of the difference in $\theta$ between the two methods and suggested that both results show the same thing: the ground state of the open system is stable against a weak perturbation.Comment: 11 pages, 5 figure

Critical thermodynamics of the two-dimensional +/-J Ising spin glass

We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that the low temperature specific heat density scales as exp(-2J/T), corresponding to an ``effective'' gap of size 2J; in addition, an associated cross-over length scale grows as exp(J/T). We justify these scalings via the degeneracy of the low-lying excitations and by the way low energy domain walls proliferate in this model

On the Effects of a Bulk Perturbation on the Ground State of 3D Ising Spin Glasses

We compute and analyze couples of ground states of 3D spin glasses before and after applying a volume perturbation which adds to the Hamiltonian a repulsion from the true ground state. The physical picture based on Replica Symmetry Breaking is in excellent agreement with the observed behavior.Comment: 4 pages including 5 .ps figure

Near optimal configurations in mean field disordered systems

We present a general technique to compute how the energy of a configuration varies as a function of its overlap with the ground state in the case of optimization problems. Our approach is based on a generalization of the cavity method to a system interacting with its ground state. With this technique we study the random matching problem as well as the mean field diluted spin glass. As a byproduct of this approach we calculate the de Almeida-Thouless transition line of the spin glass on a fixed connectivity random graph.Comment: 13 pages, 7 figure

Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition

We study the three-spin model and the Ising spin glass in a field using Migdal-Kadanoff approximation. The flows of the couplings and fields indicate no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behaviour for strong values of the couplings. We also evaluated a quantity that is a measure of the degree of non-self-averaging, and we found that it can become large for certain ranges of the parameters and the system sizes. For the spin glass in a field the maximum of non-self-averaging follows for given system size a line that resembles the de Almeida-Thouless line. We conclude that non-self-averaging found in Monte-Carlo simulations cannot be taken as evidence for the existence of a low-temperature phase with replica-symmetry breaking. Models similar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field level resembles the mode-coupling theory of real glasses. At that level the one-step replica symmetry approach breaking predicts two transitions, the first transition being dynamical and the second thermodynamical. Our results suggest that in real finite dimensional glasses there will be no genuine transitions at all, but that some features of mean-field theory could still provide some useful insights.Comment: 11 pages, 11 figure

Renormalization for Discrete Optimization

The renormalization group has proven to be a very powerful tool in physics for treating systems with many length scales. Here we show how it can be adapted to provide a new class of algorithms for discrete optimization. The heart of our method uses renormalization and recursion, and these processes are embedded in a genetic algorithm. The system is self-consistently optimized on all scales, leading to a high probability of finding the ground state configuration. To demonstrate the generality of such an approach, we perform tests on traveling salesman and spin glass problems. The results show that our ``genetic renormalization algorithm'' is extremely powerful.Comment: 4 pages, no figur

Energetics and geometry of excitations in random systems

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 perturbations. The numerical data support the assumptions of compact droplets and a single exponent for droplet energy scaling. Analytic calculations show how strong corrections to power laws can result when samples and droplets are averaged over. Such corrections can explain apparent discrepancies in several previous numerical results for spin glasses.Comment: 4 pages, eps files include