10 research outputs found
Exploring first-order phase transitions with population annealing
Population annealing is a hybrid of sequential and Markov chain Monte Carlo
methods geared towards the efficient parallel simulation of systems with
complex free-energy landscapes. Systems with first-order phase transitions are
among the problems in computational physics that are difficult to tackle with
standard methods such as local-update simulations in the canonical ensemble,
for example with the Metropolis algorithm. It is hence interesting to see
whether such transitions can be more easily studied using population annealing.
We report here our preliminary observations from population annealing runs for
the two-dimensional Potts model with , where it undergoes a first-order
transition.Comment: 10 pages, 3 figures, 3 table
Population annealing: Massively parallel simulations in statistical physics
The canonical technique for Monte Carlo simulations in statistical physics is importance sampling via a suitably constructed Markov chain. While such approaches are quite successful, they are not particularly well suited for parallelization as the chain dynamics is sequential, and if replicated chains are used to increase statistics each of them relaxes into equilibrium with an intrinsic time constant that cannot be reduced by parallel work. Population annealing is a sequential Monte Carlo method that simulates an ensemble of system replica under a cooling protocol. The population element makes it naturally well suited for massively parallel simulations, and bias can be systematically reduced by increasing the population size. We present an implementation of population annealing on graphics processing units and discuss its behavior for different systems undergoing continuous and first-order phase transitions
Estimating the Density of States of Frustrated Spin Systems
Estimating the density of states of systems with rugged free energy
landscapes is a notoriously difficult task of the utmost importance in many
areas of physics ranging from spin glasses to biopolymers. Density of states
estimation has also recently become an indispensable tool for the benchmarking
of quantum annealers when these function as samplers. Some of the standard
approaches suffer from a spurious convergence of the estimates to metastable
minima, and these cases are particularly hard to detect. Here, we introduce a
sampling technique based on population annealing enhanced with a
multi-histogram analysis and report on its performance for spin glasses. We
demonstrate its ability to overcome the pitfalls of other entropic samplers,
resulting in some cases in large scaling advantages that can lead to the
uncovering of new physics. The new technique avoids some inherent difficulties
in established approaches and can be applied to a wide range of systems without
relevant tailoring requirements. Benchmarking of the studied techniques is
facilitated by the introduction of several schemes that allow us to achieve
exact counts of the degeneracies of the tested instances.Comment: 32 pages, 11 figures, 1 tabl
GPU accelerated population annealing algorithm
Population annealing is a promising recent approach for Monte Carlo
simulations in statistical physics, in particular for the simulation of systems
with complex free-energy landscapes. It is a hybrid method, combining
importance sampling through Markov chains with elements of sequential Monte
Carlo in the form of population control. While it appears to provide
algorithmic capabilities for the simulation of such systems that are roughly
comparable to those of more established approaches such as parallel tempering,
it is intrinsically much more suitable for massively parallel computing. Here,
we tap into this structural advantage and present a highly optimized
implementation of the population annealing algorithm on GPUs that promises
speed-ups of several orders of magnitude as compared to a serial implementation
on CPUs. While the sample code is for simulations of the 2D ferromagnetic Ising
model, it should be easily adapted for simulations of other spin models,
including disordered systems. Our code includes implementations of some
advanced algorithmic features that have only recently been suggested, namely
the automatic adaptation of temperature steps and a multi-histogram analysis of
the data at different temperatures.Comment: 12 pages, 3 figures and 5 tables, code at
https://github.com/LevBarash/PAisin
GPU-Accelerated Population Annealing Algorithm: Frustrated Ising Antiferromagnet on the Stacked Triangular Lattice
The population annealing algorithm is a novel approach to study systems with rough free-energy landscapes, such as spin glasses. It combines the power of simulated annealing, Boltzmann weighted differential reproduction and sequential Monte Carlo process to bring the population of replicas to the equilibrium even in the low-temperature region. Moreover, it provides a very good estimate of the free energy. The fact that population annealing algorithm is performed over a large number of replicas with many spin updates, makes it a good candidate for massive parallelism. We chose the GPU programming using a CUDA implementation to create a highly optimized simulation. It has been previously shown for the frustrated Ising antiferromagnet on the stacked triangular lattice with a ferromagnetic interlayer coupling, that standard Markov Chain Monte Carlo simulations fail to equilibrate at low temperatures due to the effect of kinetic freezing of the ferromagnetically ordered chains. We applied the population annealing to study the case with the isotropic intra- and interlayer antiferromagnetic coupling (J2/|J1| = −1). The reached ground states correspond to non-magnetic degenerate states, where chains are antiferromagnetically ordered, but there is no long-range ordering between them, which is analogical with Wannier phase of the 2D triangular Ising antiferromagnet
Population annealing: Massively parallel simulations in statistical physics
The canonical technique for Monte Carlo simulations in statistical physics is importance sampling via a suitably constructed Markov chain. While such approaches are quite successful, they are not particularly well suited for parallelization as the chain dynamics is sequential, and if replicated chains are used to increase statistics each of them relaxes into equilibrium with an intrinsic time constant that cannot be reduced by parallel work. Population annealing is a sequential Monte Carlo method that simulates an ensemble of system replica under a cooling protocol. The population element makes it naturally well suited for massively parallel simulations, and bias can be systematically reduced by increasing the population size. We present an implementation of population annealing on graphics processing units and discuss its behavior for different systems undergoing continuous and first-order phase transitions
Population annealing: Massively parallel simulations in statistical physics
The canonical technique for Monte Carlo simulations in statistical physics is importance sampling via a suitably constructed Markov chain. While such approaches are quite successful, they are not particularly well suited for parallelization as the chain dynamics is sequential, and if replicated chains are used to increase statistics each of them relaxes into equilibrium with an intrinsic time constant that cannot be reduced by parallel work. Population annealing is a sequential Monte Carlo method that simulates an ensemble of system replica under a cooling protocol. The population element makes it naturally well suited for massively parallel simulations, and bias can be systematically reduced by increasing the population size. We present an implementation of population annealing on graphics processing units and discuss its behavior for different systems undergoing continuous and first-order phase transitions
Influence of fluid flows on electric double layers in evaporating colloidal sessile droplets
A model is developed for describing the transport of charged colloidal particles in an evaporating sessile droplet on the electrified metal substrate in the presence of a solvent flow. The model takes into account the electric charge of colloidal particles and small ions produced by electrolytic dissociation of the active groups on the colloidal particles and solvent molecules. We employ a system of self-consistent Poisson and Nernst–Planck equations for electric potential and average concentrations of colloidal particles and ions with the appropriate boundary conditions. The fluid dynamics, temperature distribution and evaporation process are described with the Navier–Stokes equations, equations of heat conduction and vapor diffusion in air, respectively. The developed model is used to carry out a first-principles numerical simulation of charged silica colloidal particle transport in an evaporating aqueous droplet. We find that electric double layers can be destroyed by a sufficiently strong fluid flow