New method for the 3D Ising model

A simple, general and practically exact method is developed for the equilibrium properties of the macroscopic physical systems with translational symmetry. Applied to the Ising model in two and three dimension, a modest calculation gives the spontaneous magnetization and the specific heat to less than 1% error

Depinning with dynamic stress overshoots: A hybrid of critical and pseudohysteretic behavior

A model of an elastic manifold driven through a random medium by an applied force F is studied focussing on the effects of inertia and elastic waves, in particular {\it stress overshoots} in which motion of one segment of the manifold causes a temporary stress on its neighboring segments in addition to the static stress. Such stress overshoots decrease the critical force for depinning and make the depinning transition hysteretic. We find that the steady state velocity of the moving phase is nevertheless history independent and the critical behavior as the force is decreased is in the same universality class as in the absence of stress overshoots: the dissipative limit which has been studied analytically. To reach this conclusion, finite-size scaling analyses of a variety of quantities have been supplemented by heuristic arguments. If the force is increased slowly from zero, the spectrum of avalanche sizes that occurs appears to be quite different from the dissipative limit. After stopping from the moving phase, the restarting involves both fractal and bubble-like nucleation. Hysteresis loops can be understood in terms of a depletion layer caused by the stress overshoots, but surprisingly, in the limit of very large samples the hysteresis loops vanish. We argue that, although there can be striking differences over a wide range of length scales, the universality class governing this pseudohysteresis is again that of the dissipative limit. Consequences of this picture for the statistics and dynamics of earthquakes on geological faults are briefly discussed.Comment: 43 pages, 57 figures (yes, that's a five followed by a seven), revte

Crossover from 2-dimensional to 1-dimensional collective pinning in NbSe3

We have fabricated NbSe$_3$ structures with widths comparable to the Fukuyama-Lee-Rice phase-coherence length. For samples already in the 2-dimensional pinning limit, we observe a crossover from 2-dimensional to 1-dimensional collective pinning when the crystal width is less than 1.6 $\mu$m, corresponding to the phase-coherence length in this direction. Our results show that surface pinning is negligible in our samples, and provide a means to probe the dynamics of single domains giving access to a new regime in charge-density wave physics.Comment: 4 pages, 2 figures, and 1 table. Accepted for publication in Physical Review

New insights into landslide processes around volcanic islands from Remotely Operated Vehicle (ROV) observations offshore Montserrat

Submarine landslide deposits have been mapped around many volcanic islands, but interpretations of their structure, composition, and emplacement are hindered by the challenges of investigating deposits directly. Here we report on detailed observations of four landslide deposits around Montserrat collected by Remotely Operated Vehicles, integrating direct imagery and sampling with sediment core and geophysical data. These complementary approaches enable a more comprehensive view of large-scale mass-wasting processes around island-arc volcanoes than has been achievable previously. The most recent landslide occurred at 11.5–14 ka (Deposit 1; 1.7 km3) and formed a radially spreading hummocky deposit that is morphologically similar to many subaerial debris-avalanche deposits. Hummocks comprise angular lava and hydrothermally altered fragments, implying a deep-seated, central subaerial collapse, inferred to have removed a major proportion of lavas from an eruptive period that now has little representation in the subaerial volcanic record. A larger landslide (Deposit 2; 10 km3) occurred at ∼130 ka and transported intact fragments of the volcanic edifice, up to 900 m across and over 100 m high. These fragments were rafted within the landslide, and are best exposed near the margins of the deposit. The largest block preserves a primary stratigraphy of subaerial volcanic breccias, of which the lower parts are encased in hemipelagic mud eroded from the seafloor. Landslide deposits south of Montserrat (Deposits 3 and 5) indicate the wide variety of debris-avalanche source lithologies around volcanic islands. Deposit 5 originated on the shallow submerged shelf, rather than the terrestrial volcanic edifice, and is dominated by carbonate debris

Extension to order β23\beta^{23} of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices

Using a renormalized linked-cluster-expansion method, we have extended to order $\beta^{23}$ the high-temperature series for the susceptibility $\chi$ and the second-moment correlation length $\xi$ of the spin-1/2 Ising models on the sc and the bcc lattices. A study of these expansions yields updated direct estimates of universal parameters, such as exponents and amplitude ratios, which characterize the critical behavior of $\chi$ and $\xi$. Our best estimates for the inverse critical temperatures are $\beta^{sc}_c=0.221654(1)$ and $\beta^{bcc}_c=0.1573725(6)$. For the susceptibility exponent we get $\gamma=1.2375(6)$ and for the correlation length exponent we get $\nu=0.6302(4)$. The ratio of the critical amplitudes of $\chi$ above and below the critical temperature is estimated to be $C_+/C_-=4.762(8)$. The analogous ratio for $\xi$ is estimated to be $f_+/f_-=1.963(8)$. For the correction-to-scaling amplitude ratio we obtain $a^+_{\xi}/a^+_{\chi}=0.87(6)$.Comment: Misprints corrected, 8 pages, latex, no figure

Adaptive cluster expansion for the inverse Ising problem: convergence, algorithm and tests

We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific clusters of variables, based on their contributions to the cross-entropy of the Ising model. Small contributions are discarded to avoid overfitting and to make the computation tractable. The properties of the cluster expansion and its performances on synthetic data are studied. To make the implementation easier we give the pseudo-code of the algorithm.Comment: Paper submitted to Journal of Statistical Physic

Bonding, Moment Formation, and Magnetic Interactions in Ca14MnBi11 and Ba14MnBi11

The ``14-1-11'' phase compounds based on magnetic Mn ions and typified by Ca14MnBi11 and Ba14MnBi11 show unusual magnetic behavior, but the large number (104) of atoms in the primitive cell has precluded any previous full electronic structure study. Using an efficient, local orbital based method within the local spin density approximation to study the electronic structure, we find a gap between a bonding valence band complex and an antibonding conduction band continuum. The bonding bands lack one electron per formula unit of being filled, making them low carrier density p-type metals. The hole resides in the MnBi4 tetrahedral unit and partially compensates the high spin d^5 Mn moment, leaving a net spin near 4 \mu_B that is consistent with experiment. These manganites are composed of two disjoint but interpenetrating `jungle gym' networks of spin 4/2 MnBi4^{9-} units with ferromagnetic interactions within the same network, and weaker couplings between the networks whose sign and magnitude is sensitive to materials parameters. Ca14MnBi11 is calculated to be ferromagnetic as observed, while for Ba14MnBi11 (which is antiferromagnetic) the ferro- and antiferromagnetic states are calculated to be essentially degenerate. The band structure of the ferromagnetic states is very close to half metallic.Comment: 17 pages, containing 10 postscript figures and 5 tables. Two additional figures (Fig.8 and 11 of the paper) are provided in JPG format in separate files. Submitted to Phys. Rev. B on September 20th 200

More is the Same; Phase Transitions and Mean Field Theories

This paper looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter", "mean field theory", and "variational method". In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor, "steam", come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in a some statistical variable of the system. The discontinuous property is called the order parameter. Each phase transitions has its own order parameter that range over a tremendous variety of physical properties. These properties include the density of a liquid gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when that jump approaches zero. This note is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of this phenomenon.Comment: 25 pages, 6 figure

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.Comment: 40 pages, final version. In publication in Phys. Rev.