Tricritical Points in Random Combinatorics: the (2+p)-SAT case

The (2+p)-Satisfiability (SAT) problem interpolates between different classes of complexity theory and is believed to be of basic interest in understanding the onset of typical case complexity in random combinatorics. In this paper, a tricritical point in the phase diagram of the random $2+p$-SAT problem is analytically computed using the replica approach and found to lie in the range $2/5 \le p_0 \le 0.416$. These bounds on $p_0$ are in agreement with previous numerical simulations and rigorous results.Comment: 7 pages, 1 figure, RevTeX, to appear in J.Phys.

Phase diagram of glassy systems in an external field

We study the mean-field phase diagram of glassy systems in a field pointing in the direction of a metastable state. We find competition among a ``magnetized'' and a ``disordered'' phase, that are separated by a coexistence line as in ordinary first order phase transitions. The coexistence line terminates in a critical point, which in principle can be observed in numerical simulations of glassy models.Comment: 4 pages, 5 figure

Universal low-temperature tricritical point in metallic ferromagnets and ferrimagnets

An earlier theory of the quantum phase transition in metallic ferromagnets is revisited and generalized in three ways. It is shown that the mechanism that leads to a fluctuation-induced first-order transition in metallic ferromagnets with a low Curie temperature is valid, (1) irrespective of whether the magnetic moments are supplied by the conduction electrons or by electrons in another band, (2) for ferromagnets in the XY and Ising universality classes as well as for Heisenberg ferromagnets, and (3) for ferrimagnets as well as for ferromagnets. This vastly expands the class of materials for which a first-order transition at low temperatures is expected, and it explains why strongly anisotropic ferromagnets, such as UGe2, display a first-order transition as well as Heisenberg magnets.Comment: 11pp, 2 fig

Metal-superconductor transition at zero temperature: A case of unusual scaling

An effective field theory is derived for the normal metal-to-superconductor quantum phase transition at T=0. The critical behavior is determined exactly for all dimensions d>2. Although the critical exponents \beta and \nu do not exist, the usual scaling relations, properly reinterpreted, still hold. A complete scaling description of the transition is given, and the physics underlying the unusual critical behavior is discussed. Quenched disorder leads to anomalously strong T_c-fluctuations which are shown to explain the experimentally observed broadening of the transition in low-T_c thin films.Comment: 4 pp., no figs, final version as publishe

The vegetation of Schouten Island, Tasmania

Thirty-seven communities defined by structure and dominance are mapped for Schouten Island which lies within the Freycinet National Park on the east coast of Tasmania. The communities dominated by herbs are mainly coastal in occurrence, those dominated by shrubs are mostly confined to the granitic east of the island, and those dominated by trees are most widespread on the dolerite and sandstone of the west. Thirteen floristic communities are recognized as a result of a monothetic divisive classification of species lists from 160 quadrats. The distribution of these communities, like that of the structure-dominance communities, is most closely related to surface geology and exposure to salt-laden winds. However, their structural expression, and to some extent their distribution, is moulded by other influences such as fire incidence and intensity, topography, and disturbances by man and other animals. Over 450 native higher plant species are recorded for the Freycinet National Park

MEDUSA - New Model of Internet Topology Using k-shell Decomposition

The k-shell decomposition of a random graph provides a different and more insightful separation of the roles of the different nodes in such a graph than does the usual analysis in terms of node degrees. We develop this approach in order to analyze the Internet's structure at a coarse level, that of the "Autonomous Systems" or ASes, the subnetworks out of which the Internet is assembled. We employ new data from DIMES (see http://www.netdimes.org), a distributed agent-based mapping effort which at present has attracted over 3800 volunteers running more than 7300 DIMES clients in over 85 countries. We combine this data with the AS graph information available from the RouteViews project at Univ. Oregon, and have obtained an Internet map with far more detail than any previous effort. The data suggests a new picture of the AS-graph structure, which distinguishes a relatively large, redundantly connected core of nearly 100 ASes and two components that flow data in and out from this core. One component is fractally interconnected through peer links; the second makes direct connections to the core only. The model which results has superficial similarities with and important differences from the "Jellyfish" structure proposed by Tauro et al., so we call it a "Medusa." We plan to use this picture as a framework for measuring and extrapolating changes in the Internet's physical structure. Our k-shell analysis may also be relevant for estimating the function of nodes in the "scale-free" graphs extracted from other naturally-occurring processes.Comment: 24 pages, 17 figure

Numerical study of a short-range p-spin glass model in three dimensions

In this work we study numerically a short range p-spin glass model in three dimensions. The behaviour of the model appears to be remarkably different from mean field predictions. In fact it shares some features typical of models with full replica-symmetry breaking (FRSB). Nevertheless, we believe that the transition that we study is intrinsically different from the FRSB and basically due to non-perturbative contributions. We study both the statics and the dynamics of the system which seem to confirm our conjectures.Comment: 20 pages, 15 figure

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one such algorithm by applying it to randomly generated, hard, instances of an NP-complete problem. For the small examples that we can simulate, the quantum adiabatic algorithm works well, and provides evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.Comment: 15 pages, 6 figures, email correspondence to [email protected] ; a shorter version of this article appeared in the April 20, 2001 issue of Science; see http://www.sciencemag.org/cgi/content/full/292/5516/47