Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session A6: Recent (algorithmic) Developments in Complex and Glass Systems |
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Sponsoring Units: DCOMP Chair: Gergely T. Zimanyi, University of California, Davis Room: Portland Ballroom 253 |
Monday, March 15, 2010 8:00AM - 8:36AM |
A6.00001: Dynamics of glassy systems using new algorithms for exact sampling on multiple scales Invited Speaker: A. Alan Middleton The complex aging and memory effects seen in glassy materials result from relaxation times that are much longer than microscopic times: direct numerical simulations that seek to reproduce these effects of course suffer from the need to run simulations for very long times. It is therefore of interest to find algorithms that will simulate nonequilbrium dynamics on very long time scales. I will present methods for rapid simulation of memory and aging effects in spin glasses and results from those simulations. The methods are based on (1) an algorithm that allows for exact sampling of equilibrium states and (2) simple coarse graining approaches to the dynamics based on exact sampling and ground state calculations. The exact sampling algorithms extend classical Pfaffian techniques to directly generate spin configurations in two-dimensional Ising spin glasses according to their Boltzmann weights, thereby avoiding the long run times needed for Markov chain Monte Carlo simulations. Equilibration can then be imposed at a chosen length scale by repeated selection of subconfigurations (patches) at that scale chosen from a larger sample. At $T=0$, memory effects can be replicated using this patchwork dynamics. Correlation functions at any temperature can also be exactly calculated. Results on thermodynamic quantities and nonequilibrium effects will be presented for samples of size at least $512^2$. This work was carried out in collaboration with Creighton K. Thomas. [Preview Abstract] |
Monday, March 15, 2010 8:36AM - 9:12AM |
A6.00002: Strengths and Weaknesses of Parallel Tempering Invited Speaker: Jon Machta Parallel tempering, also known as replica exchange Monte Carlo, is widely used for studying glassy systems with complex free energy landscapes. In this talk I will describe parallel tempering and then discuss its utility for systems with various free energy landscapes. For some simple model free energy landscapes the performance of parallel tempering can be analyzed and the results highlight strengths and weaknesses of the method. Parallel tempering is effective in overcoming free energy barriers but not in finding equilibrium states with small basins of attraction. The method is particularly effective when states separated by barriers have significantly different free energies. The relevance of these result for simulations of spin glasses using parallel tempering will be discussed. [Preview Abstract] |
Monday, March 15, 2010 9:12AM - 9:48AM |
A6.00003: New insights from one-dimensional spin glasses Invited Speaker: Helmut G. Katzgraber Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, despite ongoing research spanning several decades, there remain many fundamental open questions. Concepts from the solution of the mean-field model, such as ergodicity breaking, aging, ultrametricity, and the existence of an instability line at finite magnetic fields known as the Almeida-Thouless line, have been applied to realistic short-range spin-glass models as well as to fields as diverse as structural biology, computer science and financial analysis. Rigorous analytical results are difficult to obtain for spin glasses, in particular for realistic short-range systems. Therefore typical studies involve large-scale numerical simulations, as well as the use of efficient algorithms and improved model systems. It is of paramount importance to understand which properties of the mean-field solution carry over to short-range systems. The use of one-dimensional spin glasses with (diluted) power-law interactions has been instrumental in elucidating the properties of spin-glass systems. Large system sizes can be simulated, and different universality classes ranging from the mean-field to the short-range case can be probed by tuning the power-law exponent of the interactions. Recent results on spin-glass problems using the aforementioned one-dimensional model are presented with special emphasis on the existence of a spin-glass state in a field. [Preview Abstract] |
Monday, March 15, 2010 9:48AM - 10:24AM |
A6.00004: Glassy phases: a possible origin of computational hardness Invited Speaker: Lenka Zdeborova Given a large set of discrete variables, and some constraints between them, is there a way to choose the variables so that all constraints are satisfied? This ``satisfiability'' problem is one of the most fundamental complex optimization problems. It also has very concrete applications, for instance in computer chip testing, or in error correcting codes. The study of random satisfiability problems has shown that the hardest instances are obtained in some range of parameters where a phase transition to a glass phase takes place. Taking satisfiability as an example, this talk will summarize some of the recent progress obtained in this field using statistical physics concepts and methods which originate in the study of spin glasses. It will discuss in particular the emergence of glass phases, how they are responsible for a dramatic slowdown of algorithms, and how analytic insight into this glassy nature can help to design new types of algorithms which solve very large constraint satisfaction problems. [Preview Abstract] |
Monday, March 15, 2010 10:24AM - 11:00AM |
A6.00005: Negative-weight percolation Invited Speaker: Alexander Hartmann We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative weights. We are interested whether there are spanning paths or loops of total negative weight. This kind of percolation problem is fundamentally different from conventional percolation problems, e.g. it does not exhibit transitivity, hence no simple definition of clusters, and several spanning paths/loops might coexist in the percolation regime at the same time. Furthermore, to study this percolation problem numerically, one has to perform a non-trivial transformation of the original graph and apply sophisticated matching algorithms. Using this approach, we study the corresponding percolation transitions on large square, hexagonal and cubic lattices for two types of disorder distributions and determine the critical exponents. The results show that negative-weight percolation is in a different universality class compared to conventional bond/site percolation. On the other hand, negative-weight percolation seems to be related to the ferromagnet/spin-glass transition of random-bond Ising systems, at least in two dimensions. Furthermore, results for diluted lattices and higher dimensions up to d=7 are presented, to address, respectively, questions of (non-)universality and the transition to mean-field behavior at the upper critical dimension. [Preview Abstract] |
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