Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session W16: General Statistical and Nonlinear Physics I |
Hide Abstracts |
Room: 401 |
Thursday, March 6, 2014 2:30PM - 2:42PM |
W16.00001: Geometric criticality in random Ising models Erica Carlson, Shuo Liu, Karin Dahmen We have recently pioneered the use of geometric cluster techniques from disordered statistical mechanics to analyze scanning probe data by mapping two-component image data to random Ising models. The method is capable of extracting information from the data about disorder, interactions, and dimension. We have already successfully applied this new technique to uncover a unification of the fundamental physics governing the multiscale pattern formation observed in two disparate strongly correlated electronic materials (cuprate superconductors and vanadium dioxide). However, because the geometric clusters which are directly accessible experimentally via scanning probes do not directly encode thermodynamic critical behavior, little is known about the general theoretical structure of geometric clusters in random Ising models, and the critical exponents associated with the geometric clusters are unknown for many of the fixed points which are key to interpreting experimental data. We discuss our recent progress on uncovering the geometric critical behavior at several fixed points in random Ising models. [Preview Abstract] |
Thursday, March 6, 2014 2:42PM - 2:54PM |
W16.00002: Flat-histogram Monte Carlo in the Classical Antiferromagnetic Ising Model G. Brown, P.A. Rikvold, D.M. Nicholson, Kh. Odbadrakh, J.-Q. Yin, M. Eisenbach, S. Miyashita Flat-histogram Monte Carlo methods, such as Wang-Landau and multicanonical sampling, are extremely useful in numerical studies of frustrated magnetic systems. Numerical tools such as windowing and discrete histograms introduce discontinuities along the continuous energy variable, which in turn introduce artifacts into the calculated density of states. We demonstrate these effects and introduce practical solutions, including ``guard regions'' with biased walks for windowing and analytic representations for histograms. The classical Ising antiferromagnet supplemented by a mean-field interaction is considered. In zero field, the allowed energies are discrete and the artifacts can be avoided in small systems by not binning. For large systems, or cases where non-zero fields are used to break the degeneracy between local energy minima, the energy becomes continuous and these artifacts must be taken into account. [Preview Abstract] |
Thursday, March 6, 2014 2:54PM - 3:06PM |
W16.00003: The three-dimensional Edwards-Anderson spin glass in an external magnetic field David Yllanes Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, in order for spin glasses to be a faithful model for general glassy physics, we need to introduce an external magnetic field to eliminate their time-reversal symmetry. Unfortunately, little is known about the critical behavior of a spin glass in a field in three spatial dimensions. We have carried out a dynamical study combining equilibrium and non-equilibrium data. In particular, using the Janus computer, we have been able to simulate one thousand samples, each with half a million spins, along a time window spanning ten orders of magnitude for several magnetic fields and temperature protocols. Our main conclusion is that the system has a clearly identifiable dynamical transition, which we discuss in terms of different possibilities for the underlying physics (from a thermodynamical spin-glass transition to a mode-coupling crossover). In fact, we are able to make quantitative connections between the Edwards-Anderson spin glass and the physics of supercooled liquids. We also discuss ongoing work in equilibrium from parallel tempering simulations. [Preview Abstract] |
Thursday, March 6, 2014 3:06PM - 3:18PM |
W16.00004: Direct evidence of reentrance in three-dimensional random-bond Ising models Helmut G. Katzgraber, Ruben S. Andrist We numerically investigate the reentrant behavior in the disorder--temperature phase diagram of the three-dimensional random-bond Ising model with a fraction $p$ of antiferromagnetic bonds using large scale Monte Carlo simulations. The two-point finite-size correlation function divided by the system size is ideally suited to pinpoint second-order phase transitions in disordered magnetic systems: Because the observable is dimensionless, data for different system sizes cross at the putative transition, up to corrections to scaling. Here we show that a direct measurement of the two-point finite-size correlation function divided by the system size down to very low temperatures shows two crossings at different temperatures for $p = 22.8$\%, therefore clearly signaling reentrant behavior in the phase diagram. This means that for a fraction $p = 22.8$\% of antiferromagnetic bonds the system undergoes two phase transitions with an ordered ferromagnetic phase existing only for intermediate temperatures. Furthermore, we attempt to probe the universality classes for both transitions via an innovative finite-size scaling analysis of the susceptibility. [Preview Abstract] |
Thursday, March 6, 2014 3:18PM - 3:30PM |
W16.00005: Barkhausen noise and the random field Ising model Jian Xu, Daniel Silevitch, Thomas Rosenbaum, Karin Dahmen We measure Barkhausen noise in the rare-earth compound Nd2Fe14B prepared with large uniaxial anisotropy. A magnetic field applied transverse to the easy axis of magnetization introduces local random fields and tunes the pinning of domains. We compare the distribution of avalanche sizes and the spectral response with and without a transverse field to characterize the effects of disorder and to test predictions for critical exponents in the random field Ising model. [Preview Abstract] |
Thursday, March 6, 2014 3:30PM - 3:42PM |
W16.00006: Average case complexity of low-dimensional Ising spin glasses Ilia Zintchenko, Matthew Hastings, Matthias Troyer Finding ground states of Ising spin glasses is a notoriously hard problem for which there is to date no known efficient general case algorithm [F.Barahona, Journal of Physics A, 15, 3241, 1982]. We present strong numerical evidence that the complexity of the average case low-dimensional spin glass is polynomial in the number of vertices. To this end we present an efficient exact solver based on local constraint satisfaction for finding ground states of this system with an average case complexity polynomial in system size, exponential in the degree of the graph and polynomial in $1/h$, where $h$ is the on-site field. Numerical studies are done in two and three dimensions, and using scaling arguments we conjecture that polynomial complexity holds. We present results for bi-modal and Gaussian distributed couplings and on-site fields and discuss boundary cases on which the complexity of the algorithm is exponential. [Preview Abstract] |
Thursday, March 6, 2014 3:42PM - 3:54PM |
W16.00007: High $\textbf{q}$-State Clock Spin Glasses in Three Dimensions and the Lyapunov Exponents of Chaotic Phases and Chaotic Phase Boundaries Efe Ilker, A. Nihat Berker Spin-glass phases, phase transitions for q-state clock models and their q infinity limit XY model in d = 3 are studied by renormalization-group (RG) that is exact for the d=3 hierarchical lattice, approximate for the cubic lattice. In addition to the chaotic rescaling behavior of the spin-glass phase, each of the two types of spin-glass phase boundaries displays, under RG, its own distinctive chaotic behavior. These chaotic RG trajectories subdivide into two categories: strong-coupling chaos (in the spin-glass phase and, distinctly, on the spinglass-ferromagnetic boundary) and intermediate-coupling chaos (on the spinglass-paramagnetic boundary). We characterize each different phase and phase boundary exhibiting chaos by its distinct calculated Lyapunov exponent. We show that under RG, chaotic trajectories and fixed distributions are equivalent. The phase diagrams of arbitrary even q-state clock spin-glass models are calculated. These, for all non-infinite q, have a finite-temperature spin-glass phase. The spin-glass phases exhibit universal ordering behavior independent of q. The spin-glass phases and the spinglass-paramagnetic boundaries respectively have universal fixed distributions, chaotic trajectories, Lyapunov exponents.In the XY limit a T=0 spin-glass phase is indicated. [Preview Abstract] |
Thursday, March 6, 2014 3:54PM - 4:06PM |
W16.00008: Applying tensor renormalization group methods to frustrated and glassy systems: advantages, limitations, and applications Zheng Zhu, Helmut G. Katzgraber We study the thermodynamic properties of the two-dimensional Edwards-Anderson Ising spin-glass model on a square lattice using the tensor renormalization group method based on a higher-order singular-value decomposition. Our estimates of the internal energy per spin agree very well with high-precision parallel tempering Monte Carlo studies, thus illustrating that the method can, in principle, be applied to frustrated magnetic systems. In particular, we discuss the necessary tuning of parameters for convergence, memory requirements, efficiency for different types of disorder, as well as advantages and limitations in comparison to conventional multicanonical and Monte Carlo methods. Extensions to higher space dimensions, as well as applications to spin glasses in a field are explored. [Preview Abstract] |
Thursday, March 6, 2014 4:06PM - 4:18PM |
W16.00009: Partial solvability from dualities: Applications to Ising models in general dimensions and universal geometrical relations S. Vaezi, Z. Nussinov, G. Ortiz We illustrate that dualities or general series expansion parameter considerations lead to an extensive set of linear constraints that {\it partially solve} or, equivalently, {\it localize the computational complexity} associated with numerous systems. As an illustration, we examine both ferromagnetic and spin-glass type Ising models on hypercubic lattices in $D \ge 3$ dimensions and show that, by virtue of dualities alone, the partition functions of these systems can be determined by explicitly computing only $\sim 1/4$ of all coefficients of their high and low temperature series . For the self-dual two-dimensional Ising model, the fraction of requisite coefficients is further halved; all remaining series coefficients are determined by trivial linear combinations of this subset. These relations lead to a large set of non-trivial geometric equalities that hold in all dimensions. [Preview Abstract] |
Thursday, March 6, 2014 4:18PM - 4:30PM |
W16.00010: Spinodal nucleation effects in heterogeneous systems with long range interactions James Silva, William Klein, Harvey Gould, Kang Liu The kinetics of phase transitions in heterogeneous systems remains an area that is not well understood due to experimental difficulties despite heterogeneous nucleation being an occurrence in real systems where impurities are a common reality. In this talk work is presented in developing an understanding of nucleation near the mean field spinodal in an Ising model modified to introduce heterogeneity to the system. The effect of heterogeneity on the critical droplet properties in this simple model is investigated. The question of using a mapping to a percolation transition is also investigated in this heterogeneous system with the goal of defining a critical droplet object allowing for a geometric interpretation of thermal fluctuations in this heterogeneous system. [Preview Abstract] |
Thursday, March 6, 2014 4:30PM - 4:42PM |
W16.00011: Dynamical theory of spin noise and relaxation - prospects for real time NMR measurements Timothy Field The dynamics of a spin system is usually calculated using the density matrix. However, the usual formulation in terms of the density matrix predicts that the signal will decay to zero, and does not address the stochastic dynamics of individual spins. Spin fluctuations are to be viewed as an intrinsic quantum mechanical property of such systems immersed in random magnetic environments, and are observed as ``spin noise'' in the absence of any radio frequency (RF) excitation. Using stochastic calculus we develop a dynamical theory of spin noise and relaxation whose origins lie in the component spin fluctuations. This entails consideration of random pure states for individual protons, and how these pure states are correctly combined when the density matrix is formulated. Both the lattice and the spins are treated quantum mechanically. Such treatment incorporates both the processes of spin-spin and (finite temperature) spin-lattice relaxation. Our results reveal the intimate connections between spin noise and conventional spin relaxation, in terms of a modified spin density (MSD), distinct from the density matrix, which is necessary to describe non-ensemble averaged properties of spin systems. With the prospect of ultra-fast digitization, the role of spin noise in real time parameter extraction for (NMR) spin systems, and the advantage over standard techniques, is of essential importance, especially for systems containing a small number of spins. In this presentation we outline prospects for harnessing the recent dynamical theory in terms of spin noise measurement, with attention to real time properties. [Preview Abstract] |
Thursday, March 6, 2014 4:42PM - 4:54PM |
W16.00012: Noise and noise reduction in coupled map lattice systems of different topologies with applications Behnam Kia, Sarvenaz Kia, John Lindner, Sudeshna Sinha, William Ditto A model will be presented to demonstrate how the effects of local noise can be controlled in a variety of topologies in coupled map lattices. Then we calculate the optimal value of coupling parameters between different nodes of the lattice to obtain the maximum amount of noise reduction. We argue that the dynamics of the coupled map lattice functions as an averaging filter to reduce noise. We study this effect in different types of networks, including globally coupled and small world networks. Different numerical simulations are presented, and it is observed that there is agreement between the theoretical predictions and numerical simulations. We compare the results of this approach with the ``majority wins'' approach where in order to obtain noise robustness, a series of similar systems operate at the same time and the result of the majority is selected as the final result. We will demonstrate that our approach gives a higher level of noise robustness compared to the ``majority wins'' technique. [Preview Abstract] |
Thursday, March 6, 2014 4:54PM - 5:06PM |
W16.00013: Dissipative Processes with Infinite Memory Elvis Geneston, Mauro Bologna, Arkadii Krokhin, Paolo Grigolini We study the process of random growth of surfaces approximating it by fractional Brownian motion (FBM) with scaling
index $H$. The diffusion trajectories generated by the ballistic deposition ($H=1/3$) and Edward-Wilkinson ($H=1/4$) models are analyzed and the distribution of time intervals between two consecutive origin re-crossings are calculated numerically. This distribution follows the inverse power-law, $\psi(\tau) \propto 1/{\tau}^{\mu}$. For pure FBM $\mu = 2-H$ if $1/3 |
Thursday, March 6, 2014 5:06PM - 5:18PM |
W16.00014: Topological supersymmetry breaking: the origin of 1/f noise Igor Ovchinnikov, Kang Wang The scientific community across disciplines is still puzzled by the mysterious phenomenon generically known as 1/f noise -- the long-range (temporal and spatial) correlations that always accompany dynamical behaviors that can be intuitively characterized as chaotic/complex. Here we discuss that within the recently proposed approximation-free cohomological (or Witten-type) Topological Field Theory of Dynamical Systems all (stochastic and deterministic) dynamical systems possess the so-called topological supersymmetry. In its turn, chaotic/complex dynamics is the result of the spontaneous breakdown of this supersymmetry and the emergence of the long-range correlations in the form of 1/f noise, butterfly effect (sensitivity to initial conditions), the power-law statistics for sandpile, neurodynamical and other avalanches, Kolmogorov power spectrum for turbulence etc. is an inevitable consequence of the Goldstone theorem. [Preview Abstract] |
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