Analysis of XY Model with Mexican-Hat Interaction on a Circle
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概要
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In this study, we analyze the macroscopic properties of a model that consists of the XY model corresponding to the phase oscillator with a constant characteristic frequency and a mexican-hat interaction, using statistical mechanics. It is necessary to examine the combination model of the XY model that can express the oscillation phenomenon and the mexican-hat interaction often used as a neural network model of lateral inhibition. As a result, we found that the model has three macroscopic states: a uniform solution, a spinning solution, and a pendulum solution. The existence of the pendulum solution was not reported when the Ising model was used instead of the XY model. Furthermore, we found that a bistable phase of these solutions appears depending on the parameters of the mexican-hat interaction.
- 2011-07-15
著者
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Uezu Tatsuya
Graduate School Of Human Culture Nara Women's University
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KIMOTO Tomoyuki
Oita National College of Technology
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Okada Masato
Graduate School Of Engineering Science Osaka University
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Kimoto Tomoyuki
Oita National College of Technology, Oita 870-0152, Japan
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