Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session B50: Statistical Mechanics: Optimization and Algorithms |
Hide Abstracts |
Sponsoring Units: GSNP Chair: Alan Middleton, Syracuse University Room: 218 |
Monday, March 2, 2015 11:15AM - 11:27AM |
B50.00001: Spontaneous emergence of autocatalytic information-coding polymers Alexei Tkachenko, Sergei Maslov Self-replicating systems based on information-coding polymers are of crucial importance in biology. They also recently emerged as a paradigm in design on nano- and micro-scales. We present a general theoretical and numerical analysis of the problem of spontaneous emergence of autocatalysis for heteropolymers capable of template-assisted ligation driven by cyclic changes in the environment. Our central result is the existence of the first order transition between the regime dominated by free monomers and that with a self-sustaining population of sufficiently long oligomers. We provide a simple mathematically tractable model that predicts the parameters for the onset of autocatalysis and the distribution of chain lengths, in terms of monomer concentration, and two fundamental rate constants. Another key result is the emergence of the kinetically-limited optimal overlap length between a template and its two substrates. Template-assisted ligation allows for heritable transmission of information encoded in oligomer sequences thus opening up the possibility of long-term memory and evolvability of such systems.\\[4pt] Research was carried out in part at the Center for Functional Nanomaterials at Brookhaven National Laboratory, which is supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886. Work at Biosciences Department was supported by US Department of Energy Office of Biological Research Grant PM-031. [Preview Abstract] |
Monday, March 2, 2015 11:27AM - 11:39AM |
B50.00002: Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions Jonathan Machta, Wenlong Wang, Helmut Katzgraber A theoretical description of the low-temperature phase of short-range spin glasses has remained elusive for decades. It is not known if there is a single pair of pure states as predicted by the droplet model, or infinitely many pure states, as predicted by mean field theory. Here we study the three-dimensional Edwards-Anderson Ising spin glass in thermal boundary conditions using population annealing Monte Carlo. In thermal boundary conditions all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights, thus minimizing finite-size corrections due to domain walls. From the relative weighting of the eight boundary conditions for each disorder instance a sample stiffness is defined, and its typical value is shown to grow with system size according to a stiffness exponent. An extrapolation to the large-system-size limit is consistent with a single pair of pure states in every volume but incompatible with the mean field, replica symmetry breaking picture. [Preview Abstract] |
Monday, March 2, 2015 11:39AM - 11:51AM |
B50.00003: Probing temperature chaos through thermal boundary conditions Wenlong Wang, Jonathan Machta, Helmut Katzgraber Using population annealing Monte Carlo, we numerically study temperature chaos in the three-dimensional Edwards-Anderson Ising spin glass using thermal boundary conditions. In thermal boundary conditions all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights, thus minimizing finite-size corrections due to domain walls. By studying salient features in the specific heat we show evidence of temperature chaos. Our results suggest that these bumps are mainly caused by system-size excitations where the free energy of two boundary conditions cross. Furthermore, we study the scaling of both entropy and energy at boundary condition crossings and find that the scaling of the energy is very different from the scaling obtained by a simple change of boundary conditions. We attribute this difference to the stronger finite-size effects induced via a simple change of boundary conditions. Finally, we show that temperature chaos occurs more frequently at higher temperatures within the spin-glass phase and for larger system sizes, while the normalized distribution function with respect to temperature is about the same for different system sizes. [Preview Abstract] |
Monday, March 2, 2015 11:51AM - 12:03PM |
B50.00004: Effective Hamiltonians of 2D Spin Glass Clusters Colin Clement, Danilo Liarte, Alan Middleton, James Sethna We have a method for directly identifying the clusters which are thought to dominate the dynamics of spin glasses. We also have a method for generating an effective Hamiltonian treating each cluster as an individual spin. We used these methods on a 2D Ising spin glass with Gaussian bonds. We study these systems by generating samples and correlation functions using a combination of Monte Carlo and high-performance numerically exact Pfaffian methods. With effective cluster Hamiltonians we can calculate the free energy asymmetry of the original clusters and perform a scaling analysis. The scaling exponents found are consistent with Domain-Wall Renormalization Group methods, and probe all length scales. We can also study the flow of these effective Hamiltonians by clustering the clustered spins, and we find that our hard spin Hamiltonians at high temperature retain accurate low-temperature fluctuations when compared to their parent models. [Preview Abstract] |
Monday, March 2, 2015 12:03PM - 12:15PM |
B50.00005: Overfrustrated and Underfrustrated Spin-Glasses in d=3 and d=2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d=2 Efe Ilker, A. Nihat Berker In spin-glass (SG) systems, frustration can be adjusted continuously and considerably, without changing the antiferromagnetic (AF) bond probability p, by using locally correlated quenched randomness, both on hypercubic and hierarchical lattices [1]. With removal of 51{\%} frustration, a SG phase occurs in d=2. With addition of 33{\%} frustration, the SG phase disappears in d=3. In general, frustration lowers the SG ordering temperature. At low temperatures, increased frustration favors the spin-glass phase (before it disappears) over ferromagnetic (F) and AF phases. When any amount of frustration is introduced, chaotic rescaling of local interactions occurs in the SG phase. Chaos increases with increasing frustration. The distinct Lyapunov exponents of all chaotic phases and phase boundaries are calculated. From entropy and specific-heat curves in d = 3, it is seen that frustration lowers in temperature the onsets of long- and short-range orders in spin-glass phases, more effectively on the former. From entropy versus p, it is seen that ground-state and low-temperature entropy already mostly sets in within the F and AF phases, before the SG phase is reached.\\[4pt] [1] E. Ilker, A.N. Berker, Phys. Rev. E 89 042139 (2014). [Preview Abstract] |
Monday, March 2, 2015 12:15PM - 12:27PM |
B50.00006: The cavity method for phase transitions in sparse reconstruction algorithms Mohammad Ramezanali, Partha Mitra, Anirvan Sengupta Compressed sensing methods are capable of reconstructing high-dimensional sparse signals using a limited amount of measurements under certain conditions. The boundaries of good performance of compressed sensing methods are associated with certain phase transitions when the number of variables go to infinity. Many compressed sensing methods are formulated as optimization problems. Usual statistical physics approach to this problem involves inventing a finite temperature version of the problem, analyzing the mean field theory via replica trick, and, then taking the zero temperature limit. Although this method has been very successful in reproducing the observations, the replica trick and the non-trivial zero temperature limit obscure the essential reasons for failure of a compressed sensing algorithm. In this work, we employ the cavity method to give an alternative derivation of the phase transitions, working solely with the zero-temperature limit and providing insight into the origin of different terms in the mean field self-consistency equations. The cavity method naturally invokes a susceptibility which is central to understanding different phases in this system, and could be generalized to a much broader class of compressed sensing problems. [Preview Abstract] |
Monday, March 2, 2015 12:27PM - 12:39PM |
B50.00007: Multiply charged monopoles in cubic dimer model Sreejith Ganesh Jaya, Stephen Powell The classical cubic dimer model is a 3D statistical mechanical system whose degrees of freedom are dimers that occupy the edges between nearest neighbour vertices of a cubic lattice. Dimer occupancies are subject to the local constraint that every vertex is associated with exactly one dimer. In the presence of an aligning interaction, it is known that the system exhibits an unconventional continuous thermal phase transition from a symmetry broken columnar phase to a Coulomb-phase. The transition is in the $\rm{NCCP^1}$ universality class, which also describes the Neel-VBS transition in the JQ model and the $S=\frac{1}{2}$ Heisenberg model with suppression of hedgehog defects. Using Monte-Carlo simulations of a pair of defects in a background of fluctuating dimers, we calculate the scaling exponents for fugacities of monopole defects of charge $Q=2$ and $3$ at this critical point. Our estimates suggest that $Q=3$ monopoles are relevant and could therefore drive the JQ model away from the $\rm{NCCP^1}$ critical point on a hexagonal lattice. [Preview Abstract] |
Monday, March 2, 2015 12:39PM - 12:51PM |
B50.00008: A matrix product state method for solving combinatorial optimization problems S.S. Pelton, C. Chamon, E.R. Mucciolo We present a method based on a matrix product state representation to solve combinatorial optimization problems. All constraints are met by mapping Boolean gates into projection operators and applying operators sequentially. The method provides exact solutions with high success probability, even in the case of frustrated systems. The computational cost of the method is controlled by the maximum relative entropy of the system. Results of numerical simulations for several types of problems will be shown and discussed. [Preview Abstract] |
Monday, March 2, 2015 12:51PM - 1:03PM |
B50.00009: Emergence by Design in Artificial Spin Ice Cristiano Nisoli, Muir Morrison, Gia-Wei Chern, Ian gilbert, Sheng Zhang, Peter Schiffer Recently a new perspective has opened in the study of frustration through the creation of artificial frustrated magnetic systems [1,2]. These materials consist of arrays of lithographically fabricated single-domain ferromagnetic nanostructures that behave like giant Ising spins, whose interactions can be controlled through appropriate choices of their geometric properties and arrangement on a (frustrated) lattice. Higher control, inclusive of genuine thermal ensembles [3-5] have replaced the earlier and coarser methods based on magnetic agitation. Dynamical versions are now being realized [4,5], characterized in real time via PEEM, revealing statistical mechanics in action. This affords implementation of new geometries [6-8], not found in nature, for dedicated bottom up design of desired emergent properties [8]. Born as a scientific toy to investigate frustration-by-design, artificial spin ice might now be used to open ``a path into an uncharted territory, a landscape of advanced functional materials in which topological effects on physical properties can be explored and harnessed.'' [9]. Ref: [1] Nature 439, 303-306 (2006) [2] Rev. Mod. Phys. 85 (4), 1473 (2013) [3] Nature 500 (7464), 553 (2013). [4] Nature Physics 9, 375--382(2013) [5] Nature Nanotechnology 9, 514 (2014) [6] New Journal of Physics 15 (4), 045009 (2013) [7] Phys. Rev. Lett. 111 (17), 177201 (2013) [8] Nature Physics, 10 (9), 670-675 (2014) [9] Nature Physics, doi:10.1038/nphys3072 (2014) [Preview Abstract] |
Monday, March 2, 2015 1:03PM - 1:15PM |
B50.00010: Large-Scale Quantization and consequences in statistical mechanics George Livadiotis Recent developments revealed the existence of a new quantization constant $\hbar_{\ast }$, similar to the Planck constant $\hbar$, but $\sim$ 12 orders of magnitude larger. Planck's constant constitutes the smallest possible phase-space parcel \textit{for individual and uncorrelated particles}, while the new quantization constant describes the smallest possible phase-space parcel \textit{for collisionless particle systems characterized by collective behavior and local correlations}. The majority of space plasmas throughout the heliosphere are such systems, but any other type of systems exhibiting collective behavior and correlations between their particles can be characterized by the large-scale quantization. Here, we discuss the consequences of this alternative phase-space scale to statistical mechanics. The generalization of the old-known Sackur-Tetrode entropic formulation for systems with local correlation is such an example. [Preview Abstract] |
Monday, March 2, 2015 1:15PM - 1:27PM |
B50.00011: Modeling the thermal conductivity and shear viscosity of mixtures of methane and n-decane under high pressure and high temperature conditions using molecular simulations John Shelton Atomistic molecular dynamics simulations were carried out at equilibrium to calculate the shear viscosity and thermal conductivity of various mixtures of methane and n-decane within the range of ambient to extreme temperature and pressure conditions (i.e. up to 500 degree F and 35,000 psi). Both a computationally efficient united-atom force field and an all-atom force field were employed in this investigation. A quantitative comparison of the results was performed against experimental values and values predicted from a high temperature - high pressure perturbed chain - statistically associated fluid theory (HPHT PC-SAFT) model. Analysis of the intermolecular structure of the fluid as well as its dynamical characteristics were performed. [Preview Abstract] |
Monday, March 2, 2015 1:27PM - 1:39PM |
B50.00012: Simultaneous determination of the free energy profile and effective dynamics along a reaction coordinate Jiong Zhang, Ioan Kosztin Often one can gain insight into the functioning of a biomolecular system by following its dynamics along a relevant reaction coordinate (RC). A proper description of the motion along the RC requires not only the determination of the corresponding free energy profile (PMF) but also the correct identification of the underlying stochastic model. While there exist several methods for determining the PMF from fast non-equilibrium pulling processes, for simplicity it is implicitly assumed that the dynamics along the RC is a simple overdamped Brownian motion with known diffusion coefficient. However, in general, the dynamics along the RC is non-Markovian that can be modeled with a generalized Langevin equation characterized by a friction memory kernel. Here we propose and demonstrate a method that permits the simultaneous determination of both PMF and friction memory kernel from fast bi-directional (forward and time-reversed) pulling processes. As a result, one can determine whether the diffusion along the RC is normal or anomalous (e.g., subdiffusion). The proposed method provides a novel approach for identifying and characterizing the effective dynamics along a RC of a biomolecular system studied by either single-molecule force microscopy or steered molecular dynamics simulations. [Preview Abstract] |
Monday, March 2, 2015 1:39PM - 1:51PM |
B50.00013: Unleashing the Power of Microcanonical Inflection-Point Analysis: The Principle of Minimal Sensitivity Kai Qi, Michael Bachmann In analogy to the principle of minimal sensitivity proposed by Stevenson for perturbative approaches in quantum field theory~[1], we generalize microcanonical inflection-point analysis~[2] by probing higher-order derivatives of the inverse temperature $\beta(E)$ for signals of transitions in finite complex systems~[3]. To illustrate the power of this analysis, we investigate adsorption properties of a simple-cubic lattice polymer model. The pseudophase diagram based on microcanonical inflection-point analysis is constructed. This example confirms the general potential of microcanonical statistical analysis for studies of pseudophase transitions for systems of finite size. \\[4pt] [1] P. M. Stevenson, Phys. Rev. D \textbf{23}, 2916 (1981).\\[0pt] [2] S. Schnabel, D. T. Seaton, D. P. Landau, and M. Bachmann, Phys. Rev. E \textbf{84}, 011127 (2011).\\[0pt] [3] K. Qi and M. Bachmann, preprint (2015). [Preview Abstract] |
Monday, March 2, 2015 1:51PM - 2:03PM |
B50.00014: Optimisation by hierarchical search Ilia Zintchenko, Matthew Hastings, Matthias Troyer Finding optimal values for a set of variables relative to a cost function gives rise to some of the hardest problems in physics, computer science and applied mathematics. Although often very simple in their formulation, these problems have a complex cost function landscape which prevents currently known algorithms from efficiently finding the global optimum. Countless techniques have been proposed to partially circumvent this problem, but an efficient method is yet to be found. We present a heuristic, general purpose approach to potentially improve the performance of conventional algorithms or special purpose hardware devices by optimising groups of variables in a hierarchical way. We apply this approach to problems in combinatorial optimisation, machine learning and other fields. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2021 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700