Critical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems

Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N × N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a...

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Veröffentlicht in:理论物理通讯:英文版 2016, Vol.65 (9), p.355-362
1. Verfasser: 李晓腾 陈晓松
Format: Artikel
Sprache:eng
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Zusammenfassung:Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N × N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λn(L, t) = Lγ/νf n(t L^1/ν), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ1, λ2 and λ6, we get the finite-size scaling form of the second moment correlation length ξ(L, t) = Lξ(tL^1/ν).It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.
ISSN:0253-6102