THESIS
2014
xi, 44 pages : illustrations (some color) ; 30 cm
Abstract
We illustrate a complex-network approach to study the phase spaces, or the microscopic
state spaces, of spin glasses. By mapping the whole ground-state phase spaces of two-dimensional
Edwards-Anderson bimodal (±J) spin glasses into networks, we discovered
various structural properties of phase spaces via complex-network analysis. The Gaussian
connectivity distributions of the phase-space networks show that the free spins
exhibit a Gaussian distribution, whose variance provide a measure of frustration., The
spectra of networks are Gaussian, which is proved to be exact when the system is large.
The phase-space networks exhibit community structures whose strength is characterized
by the modularity. In addition, we find the community structure of phase-space
networks dramatically c...[
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We illustrate a complex-network approach to study the phase spaces, or the microscopic
state spaces, of spin glasses. By mapping the whole ground-state phase spaces of two-dimensional
Edwards-Anderson bimodal (±J) spin glasses into networks, we discovered
various structural properties of phase spaces via complex-network analysis. The Gaussian
connectivity distributions of the phase-space networks show that the free spins
exhibit a Gaussian distribution, whose variance provide a measure of frustration., The
spectra of networks are Gaussian, which is proved to be exact when the system is large.
The phase-space networks exhibit community structures whose strength is characterized
by the modularity. In addition, we find the community structure of phase-space
networks dramatically changes at the glass transition point where the concentration of
anti-ferromagnetic bond is 0.103. Moreover, the phase-space networks exhibit fractal
structures, which provide a real example of the conjecture that systems with long-range
correlations have fractal phase spaces. These quantitative measurements of the ground
states cast new light to the study of spin glasses. On the other hand, the phase-space
networks of spin glasses share some common features with those of lattice gases and
geometrically frustrated spin systems and establish a new class of complex networks
with unique topology.
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