Critical behavior of the Random-Field Ising Magnet with long range correlated disorder

We study the correlated-disorder driven zero-temperature phase transition of the Random-Field Ising Magnet using exact numerical ground-state calculations for cubic lattices. We consider correlations of the quenched disorder decaying proportional to r^a, where r is the distance between two lattice sites and a<0. To obtain exact ground states, we use a well established mapping to the graph-theoretical maximum-flow problem, which allows us to study large system sizes of more than two million spins. We use finite-size scaling analyses for values a={-1,-2,-3,-7} to calculate the critical point and the critical exponents characterizing the behavior of the specific heat, magnetization, susceptibility and of the correlation length close to the critical point. We find basically the same critical behavior as for the RFIM with delta-correlated disorder, except for the finite-size exponent of the susceptibility and for the case a=-1, where the results are also compatible with a phase transition at infinitesimal disorder strength. A summary of this work can be found at the papercore database at www.papercore.org.Comment: 9 pages, 13 figure

Faster algorithms for the shortest path problem

We investigate efficient implementations of Dijkstra\u27s shortest path algorithm. We propose a new data structure, called the redistributive heap, for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C, a one-level form of redistributive heap gives a time bound for Dijkstra\u27s algorithm of O(m + nlogC). A two-level form of redistributive heap gives a bound of O(m + nlogC/loglogC). A combination of a redistributive heap and a previously known data structure called a Fibonacci heap gives a bound of O(m+ nsqrt{log C}). The best previously known bounds are O(m + nlogn) using Fibonacci heaps alone and O(mloglogC) using the priority queue structure of Van Emde Boas, Kaas, and Zijlstra

Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model

We study ground-state properties of the two-dimensional random-bond Ising model with couplings having a concentration $p\in[0,1]$ of antiferromagnetic and $(1-p)$ of ferromagnetic bonds. We apply an exact matching algorithm which enables us the study of systems with linear dimension $L$ up to 700. We study the behavior of the domain-wall energies and of the magnetization. We find that the paramagnet-ferromagnet transition occurs at $p_c \sim 0.103$ compared to the concentration $p_n\sim 0.109$ at the Nishimory point, which means that the phase diagram of the model exhibits a reentrance. Furthermore, we find no indications for an (intermediate) spin-glass ordering at finite temperature.Comment: 7 pages, 12 figures, revTe

Reduction of Two-Dimensional Dilute Ising Spin Glasses

The recently proposed reduction method is applied to the Edwards-Anderson model on bond-diluted square lattices. This allows, in combination with a graph-theoretical matching algorithm, to calculate numerically exact ground states of large systems. Low-temperature domain-wall excitations are studied to determine the stiffness exponent y_2. A value of y_2=-0.281(3) is found, consistent with previous results obtained on undiluted lattices. This comparison demonstrates the validity of the reduction method for bond-diluted spin systems and provides strong support for similar studies proclaiming accurate results for stiffness exponents in dimensions d=3,...,7.Comment: 7 pages, RevTex4, 6 ps-figures included, for related information, see http://www.physics.emory.edu/faculty/boettcher

A Planarity Test via Construction Sequences

Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple reduction from planarity testing to the problem of computing a certain construction of a 3-connected graph. The approach is different from previous planarity tests; as key concept, we maintain a planar embedding that is 3-connected at each point in time. The algorithm runs in linear time and computes a planar embedding if the input graph is planar and a Kuratowski-subdivision otherwise

Ground-State and Domain-Wall Energies in the Spin-Glass Region of the 2D ±J\pm J Random-Bond Ising Model

The statistics of the ground-state and domain-wall energies for the two-dimensional random-bond Ising model on square lattices with independent, identically distributed bonds of probability $p$ of $J_{ij}= -1$ and $(1-p)$ of $J_{ij}= +1$ are studied. We are able to consider large samples of up to $320^2$ spins by using sophisticated matching algorithms. We study $L \times L$ systems, but we also consider $L \times M$ samples, for different aspect ratios $R = L / M$. We find that the scaling behavior of the ground-state energy and its sample-to-sample fluctuations inside the spin-glass region ($p_c \le p \le 1 - p_c$) are characterized by simple scaling functions. In particular, the fluctuations exhibit a cusp-like singularity at $p_c$. Inside the spin-glass region the average domain-wall energy converges to a finite nonzero value as the sample size becomes infinite, holding $R$ fixed. Here, large finite-size effects are visible, which can be explained for all $p$ by a single exponent $\omega\approx 2/3$, provided higher-order corrections to scaling are included. Finally, we confirm the validity of aspect-ratio scaling for $R \to 0$: the distribution of the domain-wall energies converges to a Gaussian for $R \to 0$, although the domain walls of neighboring subsystems of size $L \times L$ are not independent.Comment: 11 pages with 15 figures, extensively revise

Attacks on quantum key distribution protocols that employ non-ITS authentication

We demonstrate how adversaries with unbounded computing resources can break Quantum Key Distribution (QKD) protocols which employ a particular message authentication code suggested previously. This authentication code, featuring low key consumption, is not Information-Theoretically Secure (ITS) since for each message the eavesdropper has intercepted she is able to send a different message from a set of messages that she can calculate by finding collisions of a cryptographic hash function. However, when this authentication code was introduced it was shown to prevent straightforward Man-In-The-Middle (MITM) attacks against QKD protocols. In this paper, we prove that the set of messages that collide with any given message under this authentication code contains with high probability a message that has small Hamming distance to any other given message. Based on this fact we present extended MITM attacks against different versions of BB84 QKD protocols using the addressed authentication code; for three protocols we describe every single action taken by the adversary. For all protocols the adversary can obtain complete knowledge of the key, and for most protocols her success probability in doing so approaches unity. Since the attacks work against all authentication methods which allow to calculate colliding messages, the underlying building blocks of the presented attacks expose the potential pitfalls arising as a consequence of non-ITS authentication in QKD-postprocessing. We propose countermeasures, increasing the eavesdroppers demand for computational power, and also prove necessary and sufficient conditions for upgrading the discussed authentication code to the ITS level.Comment: 34 page

Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems

We consider geometric instances of the Maximum Weighted Matching Problem (MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000 vertices. Making use of a geometric duality relationship between MWMP, MTSP, and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields in near-linear time solutions as well as upper bounds. Using various computational tools, we get solutions within considerably less than 1% of the optimum. An interesting feature of our approach is that, even though an FWP is hard to compute in theory and Edmonds' algorithm for maximum weighted matching yields a polynomial solution for the MWMP, the practical behavior is just the opposite, and we can solve the FWP with high accuracy in order to find a good heuristic solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental Algorithms, 200

A transfer matrix approach to the enumeration of plane meanders

A closed plane meander of order $n$ is a closed self-avoiding curve intersecting an infinite line $2n$ times. Meanders are considered distinct up to any smooth deformation leaving the line fixed. We have developed an improved algorithm, based on transfer matrix methods, for the enumeration of plane meanders. While the algorithm has exponential complexity, its rate of growth is much smaller than that of previous algorithms. The algorithm is easily modified to enumerate various systems of closed meanders, semi-meanders, open meanders and many other geometries.Comment: 13 pages, 9 eps figures, to appear in J. Phys.

Hot dense capsule implosion cores produced by z-pinch dynamic hohlraum radiation

Hot dense capsule implosions driven by z-pinch x-rays have been measured for the first time. A ~220 eV dynamic hohlraum imploded 1.7-2.1 mm diameter gas-filled CH capsules which absorbed up to ~20 kJ of x-rays. Argon tracer atom spectra were used to measure the Te~ 1keV electron temperature and the ne ~ 1-4 x10^23 cm-3 electron density. Spectra from multiple directions provide core symmetry estimates. Computer simulations agree well with the peak compression values of Te, ne, and symmetry, indicating reasonable understanding of the hohlraum and implosion physics.Comment: submitted to Phys. Rev. Let