Publications (22)
High Resolution Study of the 2D ANNNI Model Using a Two-replica Cluster Algorithm and Population Annealing
Shane Keiser, Jon Machta
The axial next-nearest-neighbor Ising (ANNNI) model in two dimensions is studied using population annealing combined with a two-replica cluster algorithm. We are able to fully reso…
Packing Squares in a Torus
Don Blair, Christian D. Santangelo, Jon Machta
The densest packings of N unit squares in a torus are studied using analytical methods as well as simulated annealing. A rich array of dense packing solutions are found: density-on…
Absence of Chaotic Size Dependence for Spin Glasses on Hierarchical Lattices
Jeffrey Gertler, Jon Machta
We investigate the question of whether chaotic size dependence occurs on hierarichical lattices and demonstrate that it is not present in these systems. Our results show that the m…
Computational Study of a Multistep Height Model
Matthew Drake, Jon Machta, Youjin Deng +2
An equilibrium random surface multistep height model proposed in [Abraham and Newman, EPL, 86, 16002 (2009)] is studied using a variant of the worm algorithm. In one limit, the mod…
Parallel Complexity of Random Boolean Circuits
Jon Machta, Simon DeDeo, Stephan Mertens +1
Random instances of feedforward Boolean circuits are studied both analytically and numerically. Evaluating these circuits is known to be a P-complete problem and thus, in the worst…
Parallel Invaded Cluster Algorithm for the Ising Model
Yongsoo Choi, Jon Machta, Pablo Tamayo +1
A parallel version of the invaded cluster algorithm is described. Results from large scale (up to 4096^2 and 512^3) simulations of the Ising model are reported. No evidence of crit…
Natural Complexity, Computational Complexity and Depth
Jon Machta
Depth is a complexity measure for natural systems of the kind studied in statistical physics and is defined in terms of computational complexity. Depth quantifies the length of the…
Population Annealing Simulations of a Binary Hard Sphere Mixture
Jared Callaham, Jon Machta
Population annealing is a sequential Monte Carlo scheme well-suited to simulating equilibrium states of systems with rough free energy landscapes. Here we use population annealing…
Monte Carlo Methods for Rough Free Energy Landscapes: Population Annealing and Parallel Tempering
Jon Machta, Richard S. Ellis
Parallel tempering and population annealing are both effective methods for simulating equilibrium systems with rough free energy landscapes. Parallel tempering, also known as repli…
Population Annealing with Weighted Averages: A Monte Carlo Method for Rough Free Energy Landscapes
Jon Machta
The population annealing algorithm introduced by Hukushima and Iba is described. Population annealing combines simulated annealing and Boltzmann weighted differential reproduction…
Structural and computational depth of diffusion limited aggregation
Dan Tillberg, Jon Machta
Diffusion limited aggregation is studied from the perspective of computational complexity. A parallel algorithm is exhibited that requires a number of steps that scales as the dept…
Cluster Monte Carlo study of multi-component fluids of the Stillinger-Helfand and Widom-Rowlinson type
Rongfeng Sun, Harvey Gould, Jon Machta +1
Phase transitions of fluid mixtures of the type introduced by Stillinger and Helfand are studied using a continuum version of the invaded cluster algorithm. Particles of the same s…
Graphical representations and cluster algorithms for critical points with fields
Oliver Redner, Jon Machta, Lincoln Chayes
A two-replica graphical representation and associated cluster algorithm is described that is applicable to ferromagnetic Ising systems with arbitrary fields. Critical points are as…
Ground states and thermal states of the random field Ising model
Yong Wu, Jon Machta
The random field Ising model is studied numerically at both zero and positive temperature. Ground states are mapped out in a region of random and external field strength. Thermal s…
Analysis and Optimization of Population Annealing
Chris Amey, Jon Machta
Population annealing is an easily parallelizable sequential Monte Carlo algorithm that is well-suited for simulating the equilibrium properties of systems with rough free energy la…
Parallel dynamics and computational complexity of the Bak-Sneppen model
Jon Machta, Xuenan Li
The parallel computational complexity of the Bak-Sneppen evolution model is studied. It is shown that Bak-Sneppen histories can be generated by a massively parallel computer in a t…
A hybrid model for the population dynamics of periodical cicadas
Jon Machta, Julie Blackwood, Andrew Noble +2
In addition to their unusually long life cycle, periodical cicadas, {\it Magicicada} spp., provide an exceptional example of spatially synchronized life stage phenology in nature.…
Chaos in spin glasses revealed through thermal boundary conditions
Wenlong Wang, Jon Machta, Helmut G. Katzgraber
We study the fragility of spin glasses to small temperature perturbations numerically using population annealing Monte Carlo. We apply thermal boundary conditions to a three-dimens…
New algorithm and results for the three-dimensional random field Ising Model
Jon Machta, Mark Newman, Lincoln Chayes
The random field Ising model with Gaussian disorder is studied using a new Monte Carlo algorithm. The algorithm combines the advantanges of the replica exchange method and the two-…
Strengths and Weaknesses of Parallel Tempering
Jon Machta
Parallel tempering, also known as replica exchange Monte Carlo, is studied in the context of two simple free energy landscapes. The first is a double well potential defined by two…
Critical dynamics of two-replica cluster algorithms
Xuenan Li, Jon Machta
The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with…
Ground state numerical study of the three-dimensional random field Ising model
Ilija Dukovski, Jon Machta
The random field Ising model in three dimensions with Gaussian random fields is studied at zero temperature for system sizes up to 60^3. For each realization of the normalized rand…