scholarly journals Analytical solution of the Monte Carlo dynamics of a simple spin-glass model

1996 ◽  
Vol 34 (3) ◽  
pp. 159-164 ◽  
Author(s):  
L. L Bonilla ◽  
F. G Padilla ◽  
G Parisi ◽  
F Ritort
Keyword(s):  
Monte Carlo ◽  
Analytical Solution ◽  
Spin Glass ◽  
Spin Glass Model ◽  
Glass Model ◽  
Monte Carlo Dynamics

scholarly journals MULTICANONICAL SPIN GLASS SIMULATIONS

1992 ◽  
Vol 03 (06) ◽  
pp. 1251-1274 ◽  
Author(s):  
BERND A. BERG ◽  
TARIK CELIK
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lower Bound ◽  
Temperature Dependence ◽  
Spin Glass ◽  
Power Law ◽  
Spin Glasses ◽  
Spin Glass Model ◽  
Glass Model ◽  
Quantities Of Interest

We report a Monte Carlo simulation of the 2D Edwards-Anderson spin glass model within the recently introduced multicanonical ensemble. Replica on lattices of size L2 up to L=48 are investigated. Once a true groundstate is found, we are able to give a lower bound on the number of statistically independent groundstates sampled. Temperature dependence of the energy, entropy and other quantities of interest are easily calculable. In particular we report the groundstate results. Our data indicate that the large L increase of the ergodicity time is reduced to an approximately V3 power law. Altogether the results suggest that the multicanonical ensemble improves the situation of simulations for spin glasses and other systems which have to cope with similar problems of conflicting constraints.

Non-Affine Deformations at a Concentration Transition in Cross-Linked Elastomers in the Light of the 3D XY Spin Glass Model

2012 ◽  
Vol 184 ◽  
pp. 387-392 ◽  
Author(s):  
L.V. Elnikova
Keyword(s):  
Monte Carlo ◽  
Spin Glass ◽  
Liquid Crystalline ◽  
Relaxation Times ◽  
Three Dimensional ◽  
Spin Glass Model ◽  
Mechanical Spectroscopy ◽  
X Ray ◽  
Smectic A ◽  
Glass Model

X-ray and mechanical spectroscopy on liquid-crystalline elastomers give evidence of rubber elasticity, which depends upon the crosslink concentration. After applied macroscopic deformations, mesoscale non-affine deformations in these systems might lead to long relaxation times. Basing on the example of the crosslink-dependent smectic A − nematic (SmA−N) transition in polysiloxanes, we propose to use the three-dimensional Villain spin glass model and reduce it to the lattice version of the three-dimensionalXYspin-glass model. By using the Monte Carlo loop algorithm in this model, we found a percolation threshold depending on the crosslink concentration.

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