title: Effect of asymmetry in a binary state on the collective behavior of a system with spatially modulated interaction and quenched randomness.
abstract: The properties of solid states, biophysical materials, neuronal circuits, and equilibrium states of a many-body system can be studied by using techniques in statistical physics. It has been common practice to represent a system composed of binary state units by using an Ising spin network where each unit has symmetric {-1,1} states. However, the asymmetry or symmetry of the binary states of the units can affect the property and ergodicity of the system, but better understanding of the quantitative difference is still needed. We compare systems of binary units with symmetric or asymmetric states. The network has spatially modulated interaction with quenched randomness. We can bridge the Ising spin network and McCulloch-Pitts neuron network and analyze the stability of the system via replica method by introducing an interpolating parameter. The effects of the asymmetry states affect the multistability of the system and the stability of replica-symmetry solutions.
authors.affiliation: Amari Research Unit, Brain Science Institute, RIKEN, 2-1 Hirosawa Wako, Saitama, Japan. hamaguchi@neuro.duke.edu
authors.forename: Kosuke
authors.initials: K
authors.lastname: Hamaguchi
authors.forename: Hiromitsu
authors.initials: H
authors.lastname: Urano
authors.forename: Masato
authors.initials: M
authors.lastname: Okada