Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in in the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize -using this extensive and exhaustive numerical study- the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.Comment: 7 pages, 4 figures, 2 tables, paper summary available at http://www.papercore.org/Kajantie2000. arXiv admin note: substantial text overlap with arXiv:1003.1591, arXiv:1005.5637, arXiv:1107.174

Spin Domains Generate Hierarchical Ground State Structure in J=+/-1 Spin Glasses

Unbiased samples of ground states were generated for the short-range Ising spin glass with Jij=+/-1, in three dimensions. Clustering the ground states revealed their hierarchical structure, which is explained by correlated spin domains, serving as cores for macroscopic zero energy "excitations".Comment: 4 pages, 5 figures, accepted to Phys. Rev. Let

RNA secondary structure design

We consider the inverse-folding problem for RNA secondary structures: for a given (pseudo-knot-free) secondary structure find a sequence that has that structure as its ground state. If such a sequence exists, the structure is called designable. We implemented a branch-and-bound algorithm that is able to do an exhaustive search within the sequence space, i.e., gives an exact answer whether such a sequence exists. The bound required by the branch-and-bound algorithm are calculated by a dynamic programming algorithm. We consider different alphabet sizes and an ensemble of random structures, which we want to design. We find that for two letters almost none of these structures are designable. The designability improves for the three-letter case, but still a significant fraction of structures is undesignable. This changes when we look at the natural four-letter case with two pairs of complementary bases: undesignable structures are the exception, although they still exist. Finally, we also study the relation between designability and the algorithmic complexity of the branch-and-bound algorithm. Within the ensemble of structures, a high average degree of undesignability is correlated to a long time to prove that a given structure is (un-)designable. In the four-letter case, where the designability is high everywhere, the algorithmic complexity is highest in the region of naturally occurring RNA.Comment: 11 pages, 10 figure

Negative-weight percolation

We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are spanning paths or loops of total negative weight. This kind of percolation problem is fundamentally different from conventional percolation problems, e.g. it does not exhibit transitivity, hence no simple definition of clusters, and several spanning paths/loops might coexist in the percolation regime at the same time. Furthermore, to study this percolation problem numerically, one has to perform a non-trivial transformation of the original graph and apply sophisticated matching algorithms. Using this approach, we study the corresponding percolation transitions on large square, hexagonal and cubic lattices for two types of disorder distributions and determine the critical exponents. The results show that negative-weight percolation is in a different universality class compared to conventional bond/site percolation. On the other hand, negative-weight percolation seems to be related to the ferromagnet/spin-glass transition of random-bond Ising systems, at least in two dimensions.Comment: v1: 4 pages, 4 figures; v2: 10 pages, 7 figures, added results, text and reference

A Systematic Analysis of Supernova Light in Gamma-Ray Burst Afterglows

We systematically reanalyzed all Gamma-Ray Burst (GRB) afterglow data published through the end of 2002, in an attempt to detect the predicted supernova light component and to gain statistical insight on its phenomenological properties. We fit the observed photometric light curves as the sum of an afterglow, an underlying host galaxy, and a supernova component. The latter is modeled using published multi-color light curves of SN 1998bw as a template. The total sample of afterglows with established redshifts contains 21 bursts (GRB 970228 - GRB 021211). For nine of these GRBs a weak supernova excess (scaled to SN 1998bw) was found, what makes this to one of the first samples of high-z core collapse supernovae. Among this sample are all bursts with redshifts less than ~0.7. These results strongly support the notion that in fact all afterglows of long-duration GRBs contain light from an associated supernova. A statistics of the physical parameters of these GRB-supernovae shows that SN 1998bw was at the bright end of its class, while it was not special with respect to its light curve shape. Finally, we have searched for a potential correlation of the supernova luminosities with the properties of the corresponding bursts and optical afterglows, but we have not found such a relation.Comment: 25 pages, 7 figures, accepted by ApJ; revised, shortened and updated compared to version 1; Title slightly changed; all figures showing individual afterglow light curves removed, as advised by the referee; conclusions unchange

Phase transitions in diluted negative-weight percolation models

We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of total negative weight. The resulting percolation problem is fundamentally different from conventional percolation, as we have seen in a previous study of this model for the undiluted case. Here, we investigate how the percolation transition is affected by additional dilution. We consider two types of dilution: either a certain fraction of edges exhibit zero weight, or a fraction of edges is even absent. We study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms. We perform a finite-size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary. We find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change of the universality class.Comment: 8 pages, 7 figure

Magnetized Non-linear Thin Shell Instability: Numerical Studies in 2D

We revisit the analysis of the Non-linear Thin Shell Instability (NTSI) numerically, including magnetic fields. The magnetic tension force is expected to work against the main driver of the NTSI -- namely transverse momentum transport. However, depending on the field strength and orientation, the instability may grow. For fields aligned with the inflow, we find that the NTSI is suppressed only when the Alfv\'en speed surpasses the (supersonic) velocities generated along the collision interface. Even for fields perpendicular to the inflow, which are the most effective at preventing the NTSI from developing, internal structures form within the expanding slab interface, probably leading to fragmentation in the presence of self-gravity or thermal instabilities. High Reynolds numbers result in local turbulence within the perturbed slab, which in turn triggers reconnection and dissipation of the excess magnetic flux. We find that when the magnetic field is initially aligned with the flow, there exists a (weak) correlation between field strength and gas density. However, for transverse fields, this correlation essentially vanishes. In light of these results, our general conclusion is that instabilities are unlikely to be erased unless the magnetic energy in clouds is much larger than the turbulent energy. Finally, while our study is motivated by the scenario of molecular cloud formation in colliding flows, our results span a larger range of applicability, from supernovae shells to colliding stellar winds.Comment: 12 pages, 17 figures, some of them at low resolution. Submitted to ApJ, comments welcom

Reply to the Comment on `Glassy Transition in a Disordered Model for the RNA Secondary Structure'

We reply to the Comment by Hartmann (cond-mat/9908132) on our paper Phys. Rev. Lett. 84 (2000) 2026 (also cond-mat/9907125).Comment: 1 page, no figures. Accepted for publication in Phys. Rev. Let

On Which Length Scales Can Temperature Exist in Quantum Systems?

We consider a regular chain of elementary quantum systems with nearest neighbor interactions and assume that the total system is in a canonical state with temperature $T$. We analyze under what condition the state factors into a product of canonical density matrices with respect to groups of $n$ subsystems each, and when these groups have the same temperature $T$. While in classical mechanics the validity of this procedure only depends on the size of the groups $n$, in quantum mechanics the minimum group size $n_{\text{min}}$ also depends on the temperature $T$! As examples, we apply our analysis to different types of Heisenberg spin chains.Comment: To appear in: Proceedings of the SPQS conference, J. Phys. Soc. Jpn. 74 (2005) Supp

Mid-infrared observations of the SGR 1900+14 error box

We report on mid-infrared observations of the compact stellar cluster located in the proximity of SGR 1900+14, and the radio/X-ray position of this soft-gamma repeater. Observations were performed in May and June of 2001 when the bursting source was in an active state. At the known radio and X-ray position of the SGR we did not detect transient mid-IR activity, although the observations were performed only hours before and after an outburst in the high-energy band.Comment: 4 pages, 3 figures, to appear in "Gamma-Ray Burst and Afterglow Astronomy 2001", Woods Hole; 5-9 Nov, 200