Mechanism of Slow Relaxation due to Screening Effect in a Frustrated System

Abstract

We study a slow relaxation process in a frustrated spin system in which a type of screening effect due to a frustrated environment plays an important role. This screening effect is attributed to the highly degenerate configurations of the frustrated environment. This slow relaxation is due to an entropy effect and is different from those due to the energy barrier observed in systems such as random ferromagnets. In the present system, even if there is no energy gap, the slow relaxation still takes place. Thus, we call this phenomenon ``entropic slowing down''. Here, we study the mechanism of entropic slowing down quantitatively in an Ising spin model with the so-called decorated bonds. The spins included in decorated bonds (decoration spins) cause a peculiar density of states, which causes on entropy-induced screening effect. We analytically estimate the time scale of the system that increases exponentially with the number of decoration spins. We demonstrate the scaling of relaxation processes using the time scale at all temperatures including the critical point.

arXiv comment16 pages, 9 figures, to appear in J. Phys. Soc. Jpn. vol.78 no.8 (2009)

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• Quantum Annealing: A New Method for Minimizing Multidimensional Functions
• Residual Energies after Slow Quantum Annealing
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