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.

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.

IMPORTANCE-SAMPLING MONTE CARLO APPROACH TO CLASSICAL SPIN SYSTEMS

1989 ◽  
Vol 03 (03) ◽  
pp. 473-483 ◽  
Author(s):  
HSING-MEI HUANG
Keyword(s):  
Monte Carlo ◽  
Magnetic Properties ◽  
Ising Model ◽  
Computer Time ◽  
Spin Systems ◽  
Thermodynamic Quantities ◽  
New Approach ◽  
Classical Spin ◽  
Monte Carlo Calculations ◽  
Fixed Energy

A new approach for carrying out static Monte Carlo calculations of thermodynamic quantities for classical spin systems is proposed. Combining the ideas of coincidence countings and importance samplings, we formulate a scheme for obtaining Γ(E), the number of states for a fixed energy E, and use Γ(E) to compute thermodynamic properties. Using the Ising model as an example, we demonstrate that our procedure leads to accurate numerical results without excessive use of computer time. We also show that the procedure is easily extended to obtaining magnetic properties of the Ising model.

Should a hotter paramagnet transform quicker to a ferromagnet? Monte Carlo simulation results for Ising model

2021 ◽  
Author(s):  
Subir K Das ◽  
Nalina Vadakkayil
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
Simulation Results ◽  
Heating Up

For quicker formation of ice, before inserting inside a refrigerator, heating up of a body of water can be beneficial. We report first observation of a counterpart of this intriguing...

scholarly journals The Ising model with Hybrid Monte Carlo

2021 ◽  
Vol 265 ◽  
pp. 107978
Author(s):  
Johann Ostmeyer ◽  
Evan Berkowitz ◽  
Thomas Luu ◽  
Marcus Petschlies ◽  
Ferenc Pittler
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Hybrid Monte Carlo

scholarly journals A Monte Carlo Method of Solving Heat Conduction Problems

1980 ◽  
Vol 102 (1) ◽  
pp. 121-125 ◽  
Author(s):  
S. K. Fraley ◽  
T. J. Hoffman ◽  
P. N. Stevens
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Monte Carlo Method ◽  
Transport Equation ◽  
Heat Conduction Equation ◽  
Analytical Techniques ◽  
Conduction Equation ◽  
Geometric Complexity ◽  
New Approach ◽  
Temperature Distributions

A new approach in the use of Monte Carlo to solve heat conduction problems is developed using a transport equation approximation to the heat conduction equation. A variety of problems is analyzed with this method and their solutions are compared to those obtained with analytical techniques. This Monte Carlo approach appears to be limited to the calculation of temperatures at specific points rather than temperature distributions. The method is applicable to the solution of multimedia problems with no inherent limitations as to the geometric complexity of the problem.

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