11 research outputs found
Enhanced magnetocaloric effect due to selective dilution in a triangular Ising antiferromagnet
We employ an effective-field theory with correlations in order to study a
magnetocaloric effect on a triangular Ising antiferromagnet, which is
selectively diluted by non-magnetic impurities on one of the three sublattices.
Such a dilution generally relieves massive degeneracy in our system and
therefore the ground-state entropy diminishes and the magnetocaloric effect
weakens at low temperatures. However, at relatively higher temperatures we can
observe significantly enhanced negative isothermal entropy changes for the
sublattice concentration .Comment: 3 pages, 5 figures, CSMAG'16 conferenc
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
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
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
Numerical Precision Effects on GPU Simulation of Massive Spatial Data, Based on the Modified Planar Rotator Model
The present research builds on a recently proposed spatial prediction method for discretized two-dimensional data, based on a suitably modified planar rotator (MPR) spin model from statistical physics. This approach maps the measured data onto interacting spins and, exploiting spatial correlations between them, which are similar to those present in geostatistical data, predicts the data at unmeasured locations. Due to the shortrange nature of the spin pair interactions in the MPR model, parallel implementation of the prediction algorithm on graphical processing units (GPUs) is a natural way of increasing its efficiency. In this work we study the effects of reduced computing precision as well as GPU-based hardware intrinsic functions on the speedup and accuracy of the MPR-based prediction and explore which aspects of the simulation can potentially benefit the most from the reduced precision. It is found that, particularly for massive data sets, a thoughtful precision setting of the GPU implementation can significantly increase the computational efficiency, while incurring little to no degradation in the prediction accuracy
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
GPU-accelerated simulation of massive spatial data based on the modified planar rotator model
Summarization: A novel Gibbs Markov random field for spatial data on Cartesian grids based on the modified planar rotator (MPR) model of statistical physics has been recently introduced for efficient and automatic interpolation of big data sets, such as satellite and radar images. The MPR model does not rely on Gaussian assumptions. Spatial correlations are captured via nearest-neighbor interactions between transformed variables. This allows vectorization of the model which, along with an efficient hybrid Monte Carlo algorithm, leads to fast execution times that scale approximately linearly with system size. The present study takes advantage of the short-range nature of the interactions between the MPR variables to parallelize the algorithm on graphics processing units (GPUs) in the Compute Unified Device Architecture programming environment. It is shown that, for the processors employed, the GPU implementation can lead to impressive computational speedups, up to almost 500 times on large grids, compared to single-processor calculations. Consequently, massive data sets comprising millions of data points can be automatically processed in less than one second on an ordinary GPU.Presented on: Mathematical Geoscience