Dynamic critical exponent of some Monte Carlo algorithms for the self-avoiding walk

1986 ◽  
Vol 19 (13) ◽  
pp. L797-L805 ◽  
Author(s):  
S Caracciolo ◽  
A D Sokal
Keyword(s):  
Monte Carlo ◽  
Critical Exponent ◽  
The Self ◽  
Monte Carlo Algorithms ◽  
Self Avoiding Walk

scholarly journals Monte Carlo Algorithms for the Fully Frustrated XY Model

1998 ◽  
Vol 09 (05) ◽  
pp. 727-736 ◽  
Author(s):  
S. Große Pawig ◽  
K. Pinn
Keyword(s):  
Monte Carlo ◽  
Critical Exponent ◽  
Heat Bath ◽  
Square Lattice ◽  
Xy Model ◽  
Single Spin ◽  
Monte Carlo Algorithms

We investigate local update algorithms for the fully frustrated XY model on a square lattice. In addition to the standard updating procedures like the Metropolis or heat bath algorithm we include overrelaxation sweeps, implemented through single spin updates that preserve the energy of the configuration. The dynamical critical exponent (of order two) stays more or less unchanged. However, the integrated autocorrelation times of the algorithm can be significantly reduced.

New Monte Carlo method for the self-avoiding walk

1985 ◽  
Vol 40 (3-4) ◽  
pp. 483-531 ◽  
Author(s):  
Alberto Berretti ◽  
Alan D. Sokal
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
The Self ◽  
Self Avoiding Walk

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.

A Lower Bound for the End-to-End Distance of the Self-Avoiding Walk

2014 ◽  
Vol 57 (1) ◽  
pp. 113-118 ◽  
Author(s):  
Neal Madras
Keyword(s):  
Lower Bound ◽  
Critical Exponent ◽  
The Self ◽  
Hypercubic Lattice ◽  
End Distance ◽  
End To End ◽  
Self Avoiding Walk

AbstractFor an N-step self-avoiding walk on the hypercubic lattice Zd, we prove that the meansquare end-to-end distance is at least N4=(3d) times a constant. This implies that the associated critical exponent v is at least 2/(3d), assuming that v exists.

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