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

A geometrical picture for finite dimensional spin glasses

A controversial issue in spin glass theory is whether mean field correctly describes 3-dimensional spin glasses. If it does, how can replica symmetry breaking arise in terms of spin clusters in Euclidean space? Here we argue that there exist system-size low energy excitations that are sponge-like, generating multiple valleys separated by diverging energy barriers. The droplet model should be valid for length scales smaller than the size of the system (theta > 0), but nevertheless there can be system-size excitations of constant energy without destroying the spin glass phase. The picture we propose then combines droplet-like behavior at finite length scales with a potentially mean field behavior at the system-size scale.Comment: 7 pages; modified references, clarifications; to appear in EP

Large-scale low-energy excitations in 3-d spin glasses

We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement with the mean field picture. Of further interest are the position-space properties of these excitations. First, our study of their topological properties show that the majority of the large-scale excitations are sponge-like. Second, when probing their geometrical properties, we find that the excitations coarsen when the system size is increased. We conclude that either finite size effects are very large even when the spin overlap q is close to zero, or the mean field picture of homogeneous excitations has to be modified.Comment: 11 pages, typos corrected, added reference

Comparing Mean Field and Euclidean Matching Problems

Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems. Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered. We first study a mean field model taking the link lengths between points to be independent random variables. For this model we find perfect agreement with the results of a replica calculation. Then we study the case where the points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d^2). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than 0.5% at d>=2. However, we argue that the Euclidean model's 1/d series expansion is beyond all orders in k of the expansion in k-link correlations.Comment: 11 pages, 1 figur

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

Yersinia enterocolitica prevalence, on fresh pork, poultry and beef meat at retail level, in France

Y. enterocolitica is a zoonotic agent, and the third bacterial cause of human entiritis in Europe. The objective of this study was to assess consumer exposure to the pathogen Y. enterocolitica through meat consumption over a one-year period, in France. In this context, the prevalence of Y. enterocolitica was established on samples of fresh pork, beef and poultry collected at retail level in France. Of the 649 samples, 5.1% (34) were positive for Y. enterocolitica. No significant difference in prevalence between the categories of fresh meat was observed: the prevalence was 5.2 % for pork, 5.2% for beef and 5.9% for poultry meat. However, tongues of pork were highly contaminated by Y. enterocolitica (12.5%) compared to other type of meat

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