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

摘要

We investigate the eigenvalue distribution of the snapshot density matrix(SDM) generated by Monte Carlo simulation for two-dimensional classical spinsystems. We find that the distribution in the high-temperature limit is wellexplained by the random-matrix theory, while that in the low-temperature limitcan be characterized by the zero-eigenvalue condensation. At the criticalpoint, we obtain the power-law distribution with a nontrivial exponent$\alpha\equiv(2-\eta)/(1-\eta)$ and the asymptotic form of the snapshotentropy, on the basis of the relationship of the SDM with the correlationfunction matrix. The aspect-ratio dependence of the SDM spectrum is alsomentioned.