scholarly journals ON THE EMERGENCE OF COLLECTIVE ORDER IN SWARMING SYSTEMS: A RECENT DEBATE

2009 ◽  
Vol 23 (18) ◽  
pp. 3661-3685 ◽  
Author(s):  
M. ALDANA ◽  
H. LARRALDE ◽  
B. VÁZQUEZ
Keyword(s):  
Phase Transition ◽  
Boundary Conditions ◽  
Numerical Results ◽  
Dynamical Phase Transition ◽  
Vicsek Model ◽  
Numerical Evidence ◽  
First Order ◽  
Dynamical Phase ◽  
Recent Debate ◽  
Order Continuous

In this work, we consider the phase transition from ordered to disordered states that occur in the Vicsek model of self-propelled particles. This model was proposed to describe the emergence of collective order in swarming systems. When noise is added to the motion of the particles, the onset of collective order occurs through a dynamical phase transition. Based on their numerical results, Vicsek and his colleagues originally concluded that this phase transition was of second order (continuous). However, recent numerical evidence seems to indicate that the phase transition might be of first order (discontinuous), thus challenging Vicsek's original results. In this work, we review the evidence supporting both aspects of this debate. We also show new numerical results indicating that the apparent discontinuity of the phase transition may in fact be a numerical artifact produced by the artificial periodicity of the boundary conditions.

DYNAMICAL PHASE TRANSITION IN THE ISING MODEL ON A SCALE-FREE NETWORK

2005 ◽  
Vol 19 (32) ◽  
pp. 4769-4776 ◽  
Author(s):  
A. KRAWIECKI
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Ising Model ◽  
Tricritical Point ◽  
System Size ◽  
Critical Parameters ◽  
Dynamical Phase Transition ◽  
First Order ◽  
Dynamical Phase ◽  
Wide Range

Dynamical phase transition in the Ising model on a Barabási–Albert network under the influence of periodic magnetic field is studied using Monte-Carlo simulations. For a wide range of the system sizes N and the field frequencies, approximate phase borders between dynamically ordered and disordered phases are obtained on a plane h (field amplitude) versus T/Tc (temperature normalized to the static critical temperature without external field, Tc∝ ln N). On these borders, second- or first-order transitions occur, for parameter ranges separated by a tricritical point. For all frequencies of the magnetic field, position of the tricritical point is shifted toward higher values of T/Tc and lower values of h with increasing system size, i.e. the range of critical parameters corresponding to the first-order transition is broadened.

scholarly journals First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories

2009 ◽  
Vol 42 (7) ◽  
pp. 075007 ◽  
Author(s):  
Juan P Garrahan ◽  
Robert L Jack ◽  
Vivien Lecomte ◽  
Estelle Pitard ◽  
Kristina van Duijvendijk ◽  
...  
Keyword(s):  
Phase Transition ◽  
Dynamical Phase Transition ◽  
First Order ◽  
Dynamical Phase

Complex network structure of flocks in the Vicsek Model with Vectorial Noise

2014 ◽  
Vol 25 (03) ◽  
pp. 1350095 ◽  
Author(s):  
Gabriel Baglietto ◽  
Ezequiel V. Albano ◽  
Julián Candia
Keyword(s):  
Phase Transition ◽  
Complex Network ◽  
Network Structure ◽  
Time Step ◽  
Vicsek Model ◽  
Disorder Phase Transition ◽  
First Order ◽  
Direction Of Movement ◽  
Long Range Ordering ◽  
Influence Of Noise

In the Vicsek Model (VM), self-driven individuals try to adopt the direction of movement of their neighbors under the influence of noise, thus leading to a noise-driven order–disorder phase transition. By implementing the so-called Vectorial Noise (VN) variant of the VM (i.e. the VM-VN model), this phase transition has been shown to be discontinuous (first-order). In this paper, we perform an extensive complex network study of VM-VN flocks and show that their topology can be described as highly clustered, assortative, and nonhierarchical. We also study the behavior of the VM-VN model in the case of "frozen flocks" in which, after the flocks are formed using the full dynamics, particle displacements are suppressed (i.e. only rotations are allowed). Under this kind of restricted dynamics, we show that VM-VN flocks are unable to support the ordered phase. Therefore, we conclude that the particle displacements at every time-step in the VM-VN dynamics are a key element needed to sustain long-range ordering throughout.

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