Deep Computation in Statistical Physics - Abstracts

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Deep Computation in Statistical Physics Workshop
organized by Cris Moore (SFI), Jon Machta (University of Massachusetts, Amherst & SFI), and Stephan Mertens (Magdeburg & SFI)
Santa Fe Institute
August 8-10, 2013

Stefan Boettcher, Emory University
“Renormalization Group for Quantum Walks with and Without Coins”
Abstract. I will demonstrate how RG can be applied to gain insights into the asymptotic behavior of QW. The fundamental goal of RG in statistical physics is the classification of dynamical behaviors in universality classes based on general principles, such as symmetries, invariances, conservation laws, etc., independent of the microscopic details. It is not obvious whether universality is a useful concept, and whether it can provide the same amount of insight and control, for QW, or even how to implement RG. Here, I present our first steps in that direction.

Koji Hukushima, University of Tokyo
“An Irreversible Monte Carlo Method for Some Spin Systems”

Eli Ben-Naim, Los Alamos National Laboratory
“Nontrivial Exponents in Record Statistics”
Abstract. I will discuss statistics of records for an ensemble of identical and independently distributed variables. I will show that first-passage probabilities associated with persistent configurations of extreme values decay algebraically with the number of variable. The decay exponents are nontrivial and can be obtained using analytic methods, as eigenvalues of integral or differential equations. I will describe in detail three problems involving superior records, inferior records, and incremental records.

Amanda Streib and Noah Streib, NIST
“A Stratified Sampling Approach to the Ising Model”
(Joint work with Isabel Beichl and Francis Sullivan) Abstract. Approximation algorithms designed to estimate the partition function of the Ising model have been the subject of intense study for many years. Jerrum and Sinclair found the only known fpras for this problem, yet the running time of their Markov chain is too large to be practical. In this talk, we introduce a new approximation method, which combines graph theory and heuristic sampling, and aims at a practical method for the estimation of the partition function and other thermodynamic quantities.

Robert Ziff, University of Michigan
“Algorithms for Percolation”
Abstract. Here we will discuss various algorithms used in studying percolation, including identifying clusters, finding thresholds, and for finding crossing probabilities. The use of hull walks for crossing and studying “pinch points” will be demonstrated. Cluster merging using the Newman-Ziff algorithm, and its use to find thresholds by crossing and wrapping probabilities will be explained. This algorithm has also proved useful in the study of explosive percolation. Another powerful algorithm is the splitting process of rare events, useful for finding very low probability events such as the probability of having multiple crossing clusters on a long rectangular system.