scholarly journals Convergent series for polynomial lattice models with complex actions

2019 ◽  
Vol 34 (30) ◽  
pp. 1950243
Author(s):  
Vasily Sazonov
Keyword(s):  
Monte Carlo ◽  
Lattice Models ◽  
Initial Approximation ◽  
Convergent Series ◽  
Two Dimensional ◽  
Complex Action ◽  
New Approach ◽  
Monte Carlo Techniques ◽  
Sign Problem ◽  
Non Gaussian

Lattice models with complex actions are important for the understanding of matter at finite densities, but not accessible by the standard Monte Carlo techniques due to the sign problem. Here, we propose a new approach aiming to avoid the complex action/sign problem, by extending the method of convergent series (CS) with a non-Gaussian initial approximation. The main properties of the new series are demonstrated on the example of the two-dimensional oscillating integral.

TACKLING THE SIGN PROBLEM

1994 ◽  
Vol 05 (02) ◽  
pp. 275-277
Author(s):  
T D Kieu ◽  
C J Griffin
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
New Approach ◽  
Statistical Errors ◽  
Sign Problem ◽  
Complex Valued ◽  
1D Complex

To tackle the sign problem in the simulations of systems having indefinite or complex-valued measures, we propose a new approach which yields statistical errors smaller than the crude Monte Carlo using absolute values of the original measures. The 1D complex-coupling Ising model is employed as an illustration.

RECURSIVE SAMPLING OF PLANAR GRAPHS AND FRACTAL PROPERTIES OF A TWO-DIMENSIONAL QUANTUM GRAVITY

1990 ◽  
Vol 01 (01) ◽  
pp. 165-179 ◽  
Author(s):  
MICHAEL E. AGISHTEIN ◽  
ALEXANDER A. MIGDAL
Keyword(s):  
Monte Carlo ◽  
Random Graphs ◽  
Planar Graphs ◽  
Two Dimensional ◽  
Cubic Graphs ◽  
New Approach ◽  
Standard Methods ◽  
Fractal Properties ◽  
Dimensional Gravity ◽  
Dynamical Triangulation

We describe a new approach to the Monte-Carlo simulations of two-dimensional gravity. Standard dynamical triangulation technique was combined with results of direct enumeration of the cubic graphs. As a result we were able to build large (128K vertices) statistically independent random graphs directly. The quantitative correspondence between our results and those obtained by standard methods has been observed. The algorithm proved to be so efficient that we were able to conduct all the simulations, which usually require the most powerful computers, on an Iris workstation. An opportunity to generate large random graphs allowed us to observe that the internal geometry of random surfaces is more complicated than simple fractals. External geometry also proved to be rather peculiar.

scholarly journals Rejection sampling for Bayesian uncertainty evaluation using the Monte Carlo techniques of GUM-S1

Metrologia ◽  
2021 ◽  
Author(s):  
Manuel Marschall ◽  
Gerd Wuebbeler ◽  
Clemens Elster
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Prior Information ◽  
Uncertainty Evaluation ◽  
Rejection Sampling ◽  
Nonlinear Functions ◽  
Software Support ◽  
Gaussian Distributions ◽  
Monte Carlo Techniques ◽  
Non Gaussian

Abstract Supplement 1 to the GUM (GUM-S1) extends the GUM uncertainty framework to nonlinear functions and non-Gaussian distributions. For this purpose, it employs a Monte Carlo method that yields a probability density function for the measurand. This Monte Carlo method has been successfully applied in numerous applications throughout metrology. However, considerable criticism has been raised against the type A uncertainty evaluation of GUM-S1. Most of the criticism could be addressed by including prior information about the measurand which, however, is beyond the scope of GUM-S1. We propose an alternative Monte Carlo method that will allow prior information about the measurand to be included. The proposed method is based on a Bayesian uncertainty evaluation and applies a simple rejection sampling approach using the Monte Carlo techniques of GUM-S1. The range of applicability of the approach is explored theoretically and in terms of examples. The results are promising, leading us to conclude that many metrological applications could benefit from this approach. Software support is provided to ease its implementation.

scholarly journals Two-Dimensional Monte Carlo Filter for a Non-Gaussian Environment

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1385
Author(s):  
Xingzi Qiang ◽  
Rui Xue ◽  
Yanbo Zhu
Keyword(s):  
Monte Carlo ◽  
Kalman Filter ◽  
Bayesian Inference ◽  
Confidence Interval ◽  
Computation Time ◽  
Sampling Interval ◽  
Gaussian Filter ◽  
Two Dimensional ◽  
Gaussian System ◽  
Non Gaussian

In a non-Gaussian environment, the accuracy of a Kalman filter might be reduced. In this paper, a two- dimensional Monte Carlo Filter is proposed to overcome the challenge of the non-Gaussian environment for filtering. The two-dimensional Monte Carlo (TMC) method is first proposed to improve the efficacy of the sampling. Then, the TMC filter (TMCF) algorithm is proposed to solve the non-Gaussian filter problem based on the TMC. In the TMCF, particles are deployed in the confidence interval uniformly in terms of the sampling interval, and their weights are calculated based on Bayesian inference. Then, the posterior distribution is described more accurately with less particles and their weights. Different from the PF, the TMCF completes the transfer of the distribution using a series of calculations of weights and uses particles to occupy the state space in the confidence interval. Numerical simulations demonstrated that, the accuracy of the TMCF approximates the Kalman filter (KF) (the error is about 10−6) in a two-dimensional linear/ Gaussian environment. In a two-dimensional linear/non-Gaussian system, the accuracy of the TMCF is improved by 0.01, and the computation time reduced to 0.067 s from 0.20 s, compared with the particle filter.

Approaches to the sign problem in lattice field theory

2016 ◽  
Vol 31 (22) ◽  
pp. 1643007 ◽  
Author(s):  
Christof Gattringer ◽  
Kurt Langfeld
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Particle Physics ◽  
Field Theories ◽  
Quantum Field Theories ◽  
First Principle ◽  
Quantum Field ◽  
Complex Action ◽  
Lattice Field ◽  
Sign Problem

Quantum field theories (QFTs) at finite densities of matter generically involve complex actions. Standard Monte Carlo simulations based upon importance sampling, which have been producing quantitative first principle results in particle physics for almost forty years, cannot be applied in this case. Various strategies to overcome this so-called sign problem or complex action problem were proposed during the last thirty years. We here review the sign problem in lattice field theories, focusing on two more recent methods: dualization to worldline type of representations and the density-of-states approach.

scholarly journals EFFECTIVE LATTICE MODELS FOR TWO-DIMENSIONAL QUANTUM ANTIFERROMAGNETS

1990 ◽  
Vol 04 (16) ◽  
pp. 1043-1052 ◽  
Author(s):  
SUBIR SACHDEV ◽  
R. JALABERT
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Effective Action ◽  
Lattice Model ◽  
Lattice Models ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Quantum Antiferromagnets ◽  
Second Order Transition ◽  
Berry Phases

We introduce a 2+1 dimensional lattice model, S0, of N complex scalars coupled to a compact U(1) gauge field as a description of quantum fluctuations in SU(N) antiferromagnets. Duality maps are used to obtain a single effective action for the Néel and spin-Peierls order parameters. We examine the phases of S0 as a function of N: the N→∞ limit can be deduced from previous work. At N=1, S0 describes monopoles and their Berry phases, spin-Peierls order, but not the Néel field: Monte-Carlo simulations show a second-order transition from a spin-Peierls phase to a Higgs phase which is the remnant of the Néel phase.

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