scholarly journals Testing algorithms for critical slowing down

2018 ◽  
Vol 175 ◽  
pp. 02008 ◽  
Author(s):  
Guido Cossu ◽  
Peter Boyle ◽  
Norman Christ ◽  
Chulwoo Jung ◽  
Andreas Jüttner ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Topological Charge ◽  
Continuum Limit ◽  
Critical Slowing Down ◽  
Gauge Fields ◽  
Hybrid Monte Carlo ◽  
Slowing Down ◽  
Testing Algorithms ◽  
New Algorithms ◽  
The Continuum

We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge.

LATTICE SPIN MODELS AND NEW ALGORITHMS — A REVIEW OF MONTE CARLO COMPUTER SIMULATIONS

1990 ◽  
Vol 01 (01) ◽  
pp. 91-117 ◽  
Author(s):  
CLIVE F. BAILLIE
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Critical Exponent ◽  
Computer Simulations ◽  
Critical Slowing Down ◽  
Spin Models ◽  
Slowing Down ◽  
Monte Carlo Algorithms ◽  
Lattice Spin Models ◽  
New Algorithms

We review Monte Carlo computer simulations of spin models — both discrete and continuous. We explain the phenomenon of critical slowing which seriously degrades the efficiency of standard local Monte Carlo algorithms such as the Metropolis algorithm near phase transitions. We then go onto describe in detail the new algorithms which ameliorate the problem of critical slowing down, and give their dynamical critical exponent values.

scholarly journals Topological sampling through windings

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
David Albandea ◽  
Pilar Hernández ◽  
Alberto Ramos ◽  
Fernando Romero-López
Keyword(s):  
Monte Carlo ◽  
Gauge Theory ◽  
Continuum Limit ◽  
Two Dimensional ◽  
Expectation Values ◽  
Hybrid Monte Carlo ◽  
Pure Gauge Theory ◽  
Fixed Topology ◽  
Autocorrelation Time ◽  
The Continuum

AbstractWe propose a modification of the Hybrid Monte Carlo (HMC) algorithm that overcomes the topological freezing of a two-dimensional U(1) gauge theory with and without fermion content. This algorithm includes reversible jumps between topological sectors – winding steps – combined with standard HMC steps. The full algorithm is referred to as winding HMC (wHMC), and it shows an improved behaviour of the autocorrelation time towards the continuum limit. We find excellent agreement between the wHMC estimates of the plaquette and topological susceptibility and the analytical predictions in the U(1) pure gauge theory, which are known even at finite $$\beta $$ β . We also study the expectation values in fixed topological sectors using both HMC and wHMC, with and without fermions. Even when topology is frozen in HMC – leading to significant deviations in topological as well as non-topological quantities – the two algorithms agree on the fixed-topology averages. Finally, we briefly compare the wHMC algorithm results to those obtained with master-field simulations of size $$L\sim 8 \times 10^3$$ L ∼ 8 × 10 3 .

Acceleration Algorithms in Monte Carlo Simulations in Statistical Physics

1991 ◽  
Vol 02 (01) ◽  
pp. 201-208
Author(s):  
ROBERT H. SWENDSEN
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Simulations ◽  
Statistical Physics ◽  
Relaxation Times ◽  
Critical Slowing Down ◽  
Cluster Approach ◽  
New Developments ◽  
Slowing Down ◽  
Thermodynamic Phase

Monte Carlo simulations of thermodynamic phase transitions are usually hampered by long relaxation times due to the phenomenon of “critical slowing down.” Using a mapping due to Fortuin and Kasteleyn, a cluster approach to Monte Carlo simulations has been developed, which greatly reduces relaxation times, improving efficiency by up to two or three orders of magnitude. New developments and extensions of this approach are also discussed.

CHIRALLY EXTENDED QUANTUM CHROMODYNAMICS

1995 ◽  
Vol 06 (05) ◽  
pp. 725-742 ◽  
Author(s):  
RICHARD C. BROWER ◽  
YUE SHEN ◽  
CHUNG-I TAN
Keyword(s):  
Quantum Chromodynamics ◽  
Quark Mass ◽  
Continuum Limit ◽  
Chiral Limit ◽  
Scalar Fields ◽  
Weak Coupling Limit ◽  
Slowing Down ◽  
Large N ◽  
Chiral Invariance ◽  
The Continuum

We propose an extended Quantum Chromodynamics (XQCD) Lagrangian in which the fermions are coupled to elementary scalar fields through a Yukawa coupling which preserves chiral invariance. Our principle motivation is to find a new lattice formulation for QCD which avoids the source of critical slowing down usually encountered as the bare quark mass is tuned to the chiral limit. The phase diagram and the weak coupling limit for XQCD are studied. They suggest a conjecture that the continuum limit of XQCD is the same as the continuum limit of conventional lattice formulation of QCD. As examples of such universality, we present the large N solutions of two prototype models for XQCD, in which the mass of the spurious pion and sigma resonance go to infinity with the cut-off. Even if the universality conjecture turns out to be false, we believe that XQCD will still be useful as a low energy effective action for QCD phenomenology on the lattice. Numerical simulations are recommended to further investigate the possible benefits of XQCD in extracting QCD predictions.

scholarly journals ABELIAN PROJECTION AND STUDIES OF GAUGE-VARIANT QUANTITIES IN THE LATTICE QCD WITHOUT GAUGE FIXING

1996 ◽  
Vol 11 (13) ◽  
pp. 1081-1093 ◽  
Author(s):  
SERGEI V. SHABANOV
Keyword(s):  
Lattice Qcd ◽  
Continuum Limit ◽  
Gluon Propagator ◽  
Lorentz Invariance ◽  
Gauge Condition ◽  
Gauge Fields ◽  
Gauge Invariant ◽  
Dynamical Reduction ◽  
Gauge Fixing ◽  
The Continuum

We suggest a new (dynamical) Abelian projection of the lattice QCD. It contains no gauge condition imposed on gauge fields so that Gribov copying is avoided. Configurations of gauge fields that turn into monopoles in the Abelian projection can be classified in a gauge-invariant way. In the continuum limit, the theory respects the Lorentz invariance. A similar dynamical reduction of the gauge symmetry is proposed for studies of gauge-variant correlators (like a gluon propagator) in the lattice QCD. Though the procedure is harder for numerical simulations, it is free of gauge-fixing artifacts, like the Gribov horizon and copies.

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