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arXiv · 1402.6767

Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems

Yukinari Imura·Tsuyoshi Okubo·Satoshi Morita·Kouichi Okunishi
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Abstract

We investigate the eigenvalue distribution of the snapshot density matrix (SDM) generated by Monte Carlo simulation for two-dimensional classical spin systems. We find that the distribution in the high-temperature limit is well explained by the random-matrix theory, while that in the low-temperature limit can be characterized by the zero-eigenvalue condensation. At the critical point, we obtain the power-law distribution with a nontrivial exponent $\alpha\equiv(2-\eta)/(1-\eta)$ and the asymptotic form of the snapshot entropy, on the basis of the relationship of the SDM with the correlation function matrix. The aspect-ratio dependence of the SDM spectrum is also mentioned.

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Yukinari Imura, Tsuyoshi Okubo, Satoshi Morita, Kouichi Okunishi. 2014-02-27. Snapshot spectrum and critical phenomenon for two-dimensional classical spin systems. https://doi.org/10.7566/jpsj.83.114002

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