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29 March 2024
 
  » arxiv » cond-mat/0502471

 Article overview


Linking physics and algorithms in the random-field Ising model
Jan H. Meinke ; A. Alan Middleton ;
Date 21 Feb 2005
Subject Disordered Systems and Neural Networks | cond-mat.dis-nn
AbstractThe energy landscape for the random-field Ising model (RFIM) is complex, yet algorithms such as the push-relabel algorithm exist for computing the exact ground state of an RFIM sample in time polynomial in the sample volume. Simulations were carried out to investigate the scaling properties of the push-relabel algorithm. The time evolution of the algorithm was studied along with the statistics of an auxiliary potential field. At very small random fields, the algorithm dynamics are closely related to the dynamics of two-species annihilation, consistent with fractal statistics for the distribution of minima in the potential (``height’’). For $d=1,2$, a correlation length diverging at zero disorder sets a cutoff scale for the magnitude of the height field; our results are most consistent with a power-law correction to the exponential scaling of the correlation length with disorder in $d=2$. Near the ferromagnetic-paramagnetic transition in $d=3$, the time to find a solution diverges with a dynamic critical exponent of $z=0.93pm0.06$ for a priority queue version and $z=0.43pm0.06$ for a first-in first-out queue version of the algorithm. The links between the evolution of auxiliary fields in algorithmic time and the static physical properties of the RFIM ground state provide insight into the physics of the RFIM and a better understanding of how the algorithm functions.
Source arXiv, cond-mat/0502471
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