Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session C28: Equilibrium Statistical Mechanics, Followed by GSNP Student Speaker Award |
Hide Abstracts |
Sponsoring Units: GSNP Chair: Robin Selinger, Kent State University Room: 336 |
Monday, March 18, 2013 2:30PM - 2:42PM |
C28.00001: Approximate Solutions in Planted 3-SAT Benjamin Hsu, Christopher Laumann, Roderich Moessner, Shivaji Sondhi In many computational settings, there exists many instances where finding a solution requires a computing time that grows exponentially in the number of variables. Concrete examples occur in combinatorial optimization problems and cryptography in computer science or glassy systems in physics. However, while exact solutions are often known to require exponential time, a related and important question is the running time required to find approximate solutions. Treating this problem as a problem in statistical physics at finite temperature, we examine the computational running time in finding approximate solutions in 3-satisfiability for randomly generated 3-SAT instances which are guaranteed to have a solution . Analytic predictions are corroborated by numerical evidence using stochastic local search algorithms. A first order transition is found in the running time of these algorithms. [Preview Abstract] |
Monday, March 18, 2013 2:42PM - 2:54PM |
C28.00002: Wang-Landau or Statistical Mechanics Gregory Brown, Donald M. Nicholson, Markus Eisenbach, Kh. Odbadrakh The Wang-Landau algorithm and its variations provide a method for estimating a self-consistent density of states -- or equivalently the entropy -- of a system with many degrees of freedom. Possible benefits from generating a self-consistent estimate of the entropy and its derivative are presented for models with both discrete and continuous values of the energy. In addition, the advantage of computing thermodynamic quantities as derivatives of the estimated entropy over summation over the density of states is shown. [Preview Abstract] |
Monday, March 18, 2013 2:54PM - 3:06PM |
C28.00003: Coarse-graining renormalization by higher-order singular value decomposition Zhiyuan Xie, Jing Chen, Mingpu Qin, Jinwei Zhu, Liping Yang, Tao Xiang We propose a novel coarse graining tensor renormalization group method based on the higher-order singular value decomposition. This method provides an accurate but low computational cost technique for studying both classical and quantum lattice models in two- or three-dimensions. We have demonstrated this method using the Ising model on the square and cubic lattices. By keeping up to 16 bond basis states, we obtain by far the most accurate numerical renormalization group results for the 3D Ising model. We have also applied the method to study the ground state as well as finite temperature properties for the two-dimensional quantum transverse Ising model and obtain the results which are consistent with published data. [Preview Abstract] |
Monday, March 18, 2013 3:06PM - 3:18PM |
C28.00004: Cluster scaling in the dilute Ising model Kang Liu, James Silva, William Klein, Harvey Gould We consider the cluster mapping method to map the critical point in a site-diluted Ising model onto a correlated site-bond percolation. First, we prove the Coniglio-Klein bond probability has the same form in the dilute Ising model with a proper chosen temperature. Then we study the cluster size distribution near the critical point in 2D dilute Ising model with long range interactions. The power law distribution of the clusters size at the critical point has the same exponent as the mean field Ising critical point, which is consistent with the Harris criterion for the long range Ising model. In addition, we apply this percolation mapping method to identify the nucleating droplet near the spinodal and it shows that the largest cluster size could be used to find the time when nucleating droplet occurs. [Preview Abstract] |
Monday, March 18, 2013 3:18PM - 3:30PM |
C28.00005: Properties of the Ising Model Density of States Robert Hosken The Ising model Density of States (DOS) is a histogram of all the Ising model microstates binned into macrostates with the same values of the energy variables, magnetism and interaction energy. When the DOS three-dimensional surface is known analytically it can be multiplied by the Boltzmann function and summed over all possible values of the energy variables to obtain the statistical mechanics partition function, Z, where Z is a function of the temperature, the single bond energy strength, and the external magnetic field. This summation becomes an integration in the thermodynamic limit, and the result is exact in the high temperature regime. Analytical expressions for the descriptive statistics of the energy variables are presented for nearest neighbor spin interactions in a linear chain, a square lattice, and a simple cubic lattice, all for the case of periodic boundary conditions. The properties considered are the moments of the variables to the fourth order: mean, variance, correlation, skewness, and kurtosis. The DOS surface has a single peak with a known location and height, and the base of the surface lies within an isosceles triangle. Examination of this triangle shows the feasible ferromagnetic and antiferromagnetic regions, and the location of the ground states. [Preview Abstract] |
Monday, March 18, 2013 3:30PM - 3:42PM |
C28.00006: Link duality: an extension of Kramers-Wannier duality Joe Mitchell, Victor Galitski Lattice duality, in the manner the famous Kramers-Wannier duality of 1941, has been thoroughly investigated. However, even now there are very simple unexplored extensions to be uncovered and utilized. We present one such by including site energies in the model Hamiltonian and examining the dual model that results. This grants a dual model with dual variables where the original model had interactions and vice versa. We can apply this extension to the Ising model and the XY model, among others, and it is doubtful that it would not be as applicable to many classical models with traditional dualities. The dual models tend to be less dependent on the lattice and interaction of the original models. Finally, we discuss the possible applicability of these extended dualities to a Kramers-Wannier like duality for fermions. [Preview Abstract] |
Monday, March 18, 2013 3:42PM - 3:54PM |
C28.00007: Magnetization plateaus in an antiferromagnetic Ising chain with single-ion anisotropy and quenched disorder Nilton Branco, Minos Neto, Jose Ricardo de Sousa, Pedro Piccini We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (binomial or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal-field and of the width of the distributions. For the binomial distribution, the number of plateaus increases, with respect to the uniform case (F. Litaiff, J. R. de Sousa, and N. S. Branco, Sol. St. Comm. {\bf 147}, 494 (2008)) and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears, as the width increases. We present also preliminary results for the behavior of the plateaus when aperiodic modulations are introduced. [Preview Abstract] |
Monday, March 18, 2013 3:54PM - 4:06PM |
C28.00008: A generalization of equipartion and virial theorems: maximum entropy derivation Gonzalo Gutierrez, Sergio Davis It is shown that, for a continuous maximum-entropy distribution obtained from an arbitrary number of simultaneous constraints, an estimator for a given conjugate variable can be constructed. Thus, we have derived a general theorem connecting the values of Lagrange multipliers in Maximunm Entropy (MaxEnt) inference to expectation values related to an arbitrary trial function. These estimators provide another tool to widen the applicability of Jaynes' formalism (E. T. Jaynes, Phys. Rev. 106, 620 (1957)), as well as insight into the interpretation of the hypervirial relations known in Statistical Mechanics for the canonical ensemble and Rugh's dynamical temperature for the microcanonical ensemble (H. H. Rugh, Phys. Rev. Lett. 78, 772 (1997); G. Rickayzen and J. G. Powles, J. Chem. Phys. 114, 4333 (2001)). Some examples to show the applicability of these new relations within and beyond standard Statistical Mechanics will be presented. [Preview Abstract] |
Monday, March 18, 2013 4:06PM - 4:18PM |
C28.00009: Random perfect lattices and the sphere packing problem Alexei Andreanov, Antonello Scardicchio We study random sets of perfect lattices in dimensions up to $d=19$. Perfect lattices are relevant for solution of lattice sphere packing problem. In fact the best lattice packing is a perfect lattice and perfect and eutactic lattices are local maxima of the packing fraction. We use a stochastic generating algorithm for perfect lattices and define a random ensemble with an effective temperature (reminiscent of a Monte Carlo simulation) to study typical properties of perfect lattices and show how as the temperature is decreased the best known packers are easily recovered. We find that the typical perfect lattices are denser than known families and propose two hypotheses for typical packing density between which we cannot distinguish: $\phi\sim 2^{-(0.84\pm 0.06) d}$ (improvement of the Minkowksi bound), and a competitor $\phi\sim d^{-a d}$ with a very small coefficient $a=0.06\pm0.04$. We also find properties of the random walk which are suggestive of a glassy system already for moderately small dimensions. [Preview Abstract] |
Monday, March 18, 2013 4:18PM - 4:30PM |
C28.00010: Statistical Mechanics and Shape Transitions in Microscopic Plates Ee Hou Yong, L. Mahadevan We investigate the statistical mechanics of elliptical plates of parabolic thickness with free boundary condition using both analytical techniques and Monte Carlo simulation. We consider the energy landscape of this system and show that plates with spontaneous Gaussian curvature exhibit two minima while plates with zero Gaussian curvature only exhibit one stable conformation. For plate that exhibits bistability, it can undergo shape transitions between the two conformation minima if the white noise is large enough. Plates with negative spontaneous Gaussian curvature are found to be more susceptible to shape changes than its positive counterparts. Our results are applicable to many disk-like objects in the microscopic world where fluctuation effects are important. [Preview Abstract] |
Monday, March 18, 2013 4:30PM - 4:42PM |
C28.00011: ABSTRACT WITHDRAWN |
Monday, March 18, 2013 4:42PM - 4:54PM |
C28.00012: Forecasting large earthquakes using small-quake correlations Braden Brinkman, Michael LeBlanc, Yehuda Ben-Zion, J.T. Uhl, Karin Dahmen It has long been speculated that periodic stress variations, such as the tides, may trigger earthquakes, and hence tide-earthquake correlations could be used as signals for predicting large earthquakes prior to failure. We developed a simple probabilistic model of earthquake triggering which we used to simulate series of earthquake events in a fault subjected to external periodic stresses of amplitudes and frequencies representative of tidal or seasonal stress variations. By analyzing correlations between small events and periodic stress cycles, we compute the probability that a large event will occur. We find that seasonal stresses are better predictors of impending large earthquakes. In addition, our results also apply to many other sheared frictional stick-slip systems which display small slips, such as rock interfaces or granular matter. [Preview Abstract] |
Monday, March 18, 2013 4:54PM - 5:06PM |
C28.00013: Graphicality of random scale-free networks with general degree cutoffs Yongjoo Baek, Daniel Kim, Meesoon Ha, Hawoong Jeong We study graphicality of random scale-free networks with arbitrary degree cutoffs in the thermodynamic limit, which refers to realizability of degree sequences randomly generated with the degree exponent $\gamma$ and the upper degree cutoff $k_c$ as the number of nodes $N$ goes to infinity. While a recent study\footnote{C. I. Del Genio, T. Gross, and K. E. Bassler, Phys. Rev. Lett. {\bf 107}, 178701 (2011).} found that only degree sequences with $\gamma > 2$ or $\gamma < 0$ are graphical if $k_c = N-1$ using the graphicality criterion proved by Erd\"os and Gallai,\footnote{P. Erd\"os and T. Gallai, Matematikai lapok {\bf 11}, 264 (1960).} we generalize the study to different upper cutoffs. To ensure graphicality of degree sequences, it is found that the upper cutoff must be lower than $k_c \sim N^{1/\gamma}$ for $\gamma < 2$, whereas any upper cutoff is allowed for $\gamma > 2$. This is also numerically verified, using both random and deterministic sampling of degree sequences. Our result can be interpreted as giving a fundamental constraint on the structure of random scale-free networks. [Preview Abstract] |
Monday, March 18, 2013 5:06PM - 5:18PM |
C28.00014: Slower recovery in space before collapse of connected populations Lei Dai, Kirill Korolev, Jeff Gore Slower recovery from perturbations near a tipping point and its indirect signatures in fluctuation patterns have been suggested to alert catastrophes in a wide variety of systems. Recent studies of populations in the field and in the laboratory have used time-series data to confirm some of the theoretically predicted early warning indicators, such as an increase in recovery time or in the size and timescale of fluctuations. However, the performance of warning signals in spatially extended systems remains to be examined empirically. Here we use spatially extended yeast populations, an experimental system displaying a fold bifurcation, to evaluate early warning signals based on spatio-temporal fluctuations and to identify a novel warning indicator in space. We found that two leading indicators based on fluctuations increased before collapse of connected populations; however, the magnitude of increase was smaller than that observed in isolated populations, possibly because local variation is reduced by dispersal. Furthermore, we propose a generic indicator based on deterministic spatial patterns, ``recovery length.'' As the spatial counterpart of recovery time, recovery length is defined as the distance for connected populations to recover from perturbations in space (e.g. a region of poor quality). In our experiments, recovery length increased substantially before population collapse, suggesting that the spatial scale of recovery can provide a superior warning signal before tipping points in spatially extended systems. [Preview Abstract] |
Monday, March 18, 2013 5:18PM - 5:30PM |
C28.00015: An exactly solvable model of Maxwell's demon Dibyendu Mandal, Christopher Jarzynski The paradox of Maxwell's demon has stimulated numerous thought experiments, leading to discussions about the thermodynamic implications of information processing. However, the field has lacked a tangible example or model of an autonomous, mechanical system that reproduces the actions of the demon. To address this issue, we introduce an explicit model of a device that can deliver work to lift a mass against gravity by rectifying thermal fluctuations, while writing information to a memory register. We solve for the steady-state behavior of the model and construct its nonequilibrium phase diagram. In addition to the engine-like action described above, we identify a ``Landauer eraser'' region in the phase diagram where the model uses externally supplied work to remove information from the memory register. Our model offers a simple paradigm for investigating the thermodynamics of information processing by exposing a transparent mechanism of operation. [Preview Abstract] |
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