Abstract
The statistical mechanical approach is a powerful method for understanding large degrees of freedom problems, such as those related to the spin-glass model, but its application is usually limited to the class of mean-field models. We try a new general and computational approach - instead of an exact calculation of the Boltzmann distribution, we use an empirical spin state distribution obtained through simulation and extract potentially useful axes by principal component analysis (PCA). We adopted a three-body Sourlas code to evaluate this PCA approach compared with existing replica theory. The empirical spin distribution projected to these PCA axes showed distinctive patterns corresponding to the phase given by the replica method. Moreover, the first principal component roughly coincided with one of the order parameters (averaged spin) under a certain condition. These results suggest that this PCA approach could be effective even in more complicated systems that we cannot investigate analytically.
| Original language | English |
|---|---|
| Pages (from-to) | 246-249 |
| Number of pages | 4 |
| Journal | Progress of Theoretical Physics Supplement |
| Volume | 157 |
| Publication status | Published - 2005 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
A PCA approach to sourlas code analysis. / Inoue, Masato; Hukushima, Koji; Okada, Masato.
In: Progress of Theoretical Physics Supplement, Vol. 157, 2005, p. 246-249.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A PCA approach to sourlas code analysis
AU - Inoue, Masato
AU - Hukushima, Koji
AU - Okada, Masato
PY - 2005
Y1 - 2005
N2 - The statistical mechanical approach is a powerful method for understanding large degrees of freedom problems, such as those related to the spin-glass model, but its application is usually limited to the class of mean-field models. We try a new general and computational approach - instead of an exact calculation of the Boltzmann distribution, we use an empirical spin state distribution obtained through simulation and extract potentially useful axes by principal component analysis (PCA). We adopted a three-body Sourlas code to evaluate this PCA approach compared with existing replica theory. The empirical spin distribution projected to these PCA axes showed distinctive patterns corresponding to the phase given by the replica method. Moreover, the first principal component roughly coincided with one of the order parameters (averaged spin) under a certain condition. These results suggest that this PCA approach could be effective even in more complicated systems that we cannot investigate analytically.
AB - The statistical mechanical approach is a powerful method for understanding large degrees of freedom problems, such as those related to the spin-glass model, but its application is usually limited to the class of mean-field models. We try a new general and computational approach - instead of an exact calculation of the Boltzmann distribution, we use an empirical spin state distribution obtained through simulation and extract potentially useful axes by principal component analysis (PCA). We adopted a three-body Sourlas code to evaluate this PCA approach compared with existing replica theory. The empirical spin distribution projected to these PCA axes showed distinctive patterns corresponding to the phase given by the replica method. Moreover, the first principal component roughly coincided with one of the order parameters (averaged spin) under a certain condition. These results suggest that this PCA approach could be effective even in more complicated systems that we cannot investigate analytically.
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M3 - Article
VL - 157
SP - 246
EP - 249
JO - Progress of Theoretical Physics
JF - Progress of Theoretical Physics
SN - 0033-068X
ER -