Reply to Comment on "Ising Spin Glasses in a Magnetic Field"

The problem of the survival of a spin glass phase in the presence of a field has been a challenging one for a long time. To date, all attempts using equilibrium Monte Carlo methods have been unconclusive. In their comment to our paper, Marinari, Parisi and Zuliani use out-of-equilibrium measurements to test for an Almeida-Thouless line. In our view such a dynamic approach is not based on very solid foundations in finite dimensional systems and so cannot be as compelling as equilibrium approaches. Nevertheless, the results of those authors suggests that there is a critical field near B=0.4 at zero temperature. In view of this quite small value (compared to the mean field value), we have reanalyzed our data. We find that if finite size scaling is to distinguish between that small field and a zero field, we would need to go to lattice sizes of about 20x20x20.Comment: reply to comment cond-mat/9812401 on ref. cond-mat/981141

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

Comment on "Ising Spin Glasses in a Magnetic Field"

In ref. cond-mat/9811419 Houdayer and Martin analyze the T=0 3d EA spin glass with a magnetic field $B$. By using a new, powerful method, they determine an effective critical field $B_c$ as a function of the lattice size $L$. They use their results to deduce that the model is behaving like in the droplet approach and not like the mean-field theory. We show here, by using some unpublished data, that this very interesting method and numerical results are completely compatible with the behavior implied by the Replica Symmetry Breaking theory.Comment: One page comment about ref. cond-mat/9811419, including two eps figure

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

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

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

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

Equilibrium valleys in spin glasses at low temperature

We investigate the 3-dimensional Edwards-Anderson spin glass model at low temperature on simple cubic lattices of sizes up to L=12. Our findings show a strong continuity among T>0 physical features and those found previously at T=0, leading to a scenario with emerging mean field like characteristics that are enhanced in the large volume limit. For instance, the picture of space filling sponges seems to survive in the large volume limit at T>0, while entropic effects play a crucial role in determining the free-energy degeneracy of our finite volume states. All of our analysis is applied to equilibrium configurations obtained by a parallel tempering on 512 different disorder realizations. First, we consider the spatial properties of the sites where pairs of independent spin configurations differ and we introduce a modified spin overlap distribution which exhibits a non-trivial limit for large L. Second, after removing the Z_2 (+-1) symmetry, we cluster spin configurations into valleys. On average these valleys have free-energy differences of O(1), but a difference in the (extensive) internal energy that grows significantly with L; there is thus a large interplay between energy and entropy fluctuations. We also find that valleys typically differ by sponge-like space filling clusters, just as found previously for low-energy system-size excitations above the ground state.Comment: 10 pages, 8 figures, RevTeX format. Clarifications and additional reference

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

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