Magnetization reversal times in the two-dimensional Ising model

Brendel, Kevin; Barkema, G. T.; Beijeren, H. van

doi:10.1103/physreve.67.026119

Cited by 15 publications

(13 citation statements)

References 8 publications

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“…We now introduce an Ising-type spin model [17,18] to better understand the impact of social conformity, anisotropy and asymmetry of interactions, and group size on the propagation Positions have been corrected so that all groups move in the same direction, with the outer wall at their right-hand side. The origin of the coordinate system is set to the centroid of the average positions of individuals.…”

Section: Modelling Collective U-turns (A) Model Descriptionmentioning

confidence: 99%

“…We now introduce an Ising-type spin model [17,18] to better understand the impact of social conformity, anisotropy and asymmetry of interactions, and group size on the propagation ) of all individuals at initiation of collective U-turns, ranked by order of turning (i.e. rank 1 is initiator) in groups of five.…”

Section: Modelling Collective U-turns (A) Model Descriptionmentioning

confidence: 99%

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Social conformity and propagation of information in collective U-turns of fish schools

et al. 2018

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Moving animal groups such as schools of fishes or flocks of birds often undergo sudden collective changes of their travelling direction as a consequence of stochastic fluctuations in heading of the individuals. However, the mechanisms by which these behavioural fluctuations arise at the individual level and propagate within a group are still unclear. In this study, we combine an experimental and theoretical approach to investigate spontaneous collective U-turns in groups of rummy-nose tetra () swimming in a ring-shaped tank. U-turns imply that fish switch their heading between the clockwise and anticlockwise direction. We reconstruct trajectories of individuals moving alone and in groups of different sizes. We show that the group decreases its swimming speed before a collective U-turn. This is in agreement with previous theoretical predictions showing that speed decrease facilitates an amplification of fluctuations in heading in the group, which can trigger U-turns. These collective U-turns are mostly initiated by individuals at the front of the group. Once an individual has initiated a U-turn, the new direction propagates through the group from front to back without amplification or dampening, resembling the dynamics of falling dominoes. The mean time between collective U-turns sharply increases as the size of the group increases. We develop an Ising spin model integrating anisotropic and asymmetrical interactions between fish and their tendency to follow the majority of their neighbours nonlinearly (social conformity). The model quantitatively reproduces key features of the dynamics and the frequency of collective U-turns observed in experiments.

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Section: Modelling Collective U-turns (A) Model Descriptionmentioning

confidence: 99%

“…We now introduce an Ising-type spin model [17,18] to better understand the impact of social conformity, anisotropy and asymmetry of interactions, and group size on the propagation ) of all individuals at initiation of collective U-turns, ranked by order of turning (i.e. rank 1 is initiator) in groups of five.…”

Section: Modelling Collective U-turns (A) Model Descriptionmentioning

confidence: 99%

Social conformity and propagation of information in collective U-turns of fish schools

et al. 2018

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“…Here, we study the influence of group size on the individual and collective propensity to change swimming direction. Ising-type spin models are of particular interest to study the time interval between directional changes for systems of various sizes [22]. Each agent i has a direction of motion d i ∈ {−1, 1} with d i = −1 representing swimming clockwise and d i = 1 swimming anticlockwise.…”

Section: Modelling Collective U-turn Dynamics In Groups Of Fishmentioning

confidence: 99%

“…We now introduce an Ising-type spin model [20,21] to better understand the impact of social conformity, anisotropy and asymmetry of interactions, and group size on the propagation of information during U-turns. Each agent i has a direction of motion d i ∈ {−1, 1} with d i = −1 representing swimming clockwise and d i = 1 swimming anticlockwise.…”

Section: Modelling Collective U-turns 41 Model Descriptionmentioning

confidence: 99%

Domino-like propagation of collective U-turns in fish schools

Lecheval

Jiang

Tichit

et al. 2017

Preprint

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Moving animal groups such as schools of fish or flocks of birds often undergo sudden collective changes of their travelling direction as a consequence of stochastic fluctuations in heading of the individuals. However, the mechanisms by which these behavioural fluctuations arise at the individual level and propagate within a group are still unclear. In the present study, we combine an experimental and theoretical approach to investigate spontaneous collective U-turns in groups of rummy-nose tetra (Hemigrammus rhodostomus) swimming in a ring-shaped tank. U-turns imply that fish switch their heading between the clockwise and anticlockwise direction. We reconstruct trajectories of individuals moving alone and in groups of different sizes. We show that the group decreases its swimming speed before a collective U-turn. This is in agreement with previous theoretical predictions showing that speed decrease facilitates an amplification of fluctuations in heading in the group, which can trigger U-turns. These collective U-turns are mostly initiated by individuals at the front of the group. Once an individual has initiated a U-turn, the new direction propagates through the group from front to back without amplification or dampening, resembling the dynamics of falling dominoes. The mean time between collective U-turns sharply increases as the size of the group increases. We develop an Ising spin model integrating anisotropic and asymmetrical interactions between fish and their tendency to follow the majority of their neighbours nonlinearly (social conformity). The model quantitatively reproduces key features of the dynamics and the frequency of collective U-turns observed in experiments.

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“…Here, we propose to verify experimentally the presence of all-to-all mean-field couplings by monitoring the time-scales of spontaneous magnetization flips below the magnetic transition. Similar effects of magnetization reversals could in principle take place in systems with only short-range interactions [12]. However, here we propose to explore the experimental conditions in which collective reversals are driven by the presence of long-range interactions, and therefore their existence becomes strongly dependent on the shape of the sample.…”

mentioning

confidence: 95%

Long-range effects in layered spin structures

Campa¹,

Khomeriki²,

Mukamel³

et al. 2007

Phys. Rev. B

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We study theoretically layered spin systems where long-range dipolar interactions play a relevant role. By choosing a specific sample shape, we are able to reduce the complex Hamiltonian of the system to that of a much simpler coupled rotator model with short-range and mean-field interactions. This latter model has been studied in the past because of its interesting dynamical and statistical properties related to exotic features of long-range interactions. It is suggested that experiments could be conducted such that within a specific temperature range the presence of long-range interactions crucially affect the behavior of the system.

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Magnetization reversal times in the two-dimensional Ising model

Cited by 15 publications

References 8 publications

Social conformity and propagation of information in collective U-turns of fish schools

Social conformity and propagation of information in collective U-turns of fish schools

Domino-like propagation of collective U-turns in fish schools

Long-range effects in layered spin structures

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