First-order like phase transition induced by quenched coupling disorder
Hong, Hyunsuk and Martens, Erik A. LU
(2022)
In Chaos
32(6).
- Abstract
We investigate the collective dynamics of a population of X Y model-type oscillators, globally coupled via non-separable interactions that are randomly chosen from a positive or negative value and subject to thermal noise controlled by temperature T. We find that the system at T = 0 exhibits a discontinuous, first-order like phase transition from the incoherent to the fully coherent state; when thermal noise is present (T > 0), the transition from incoherence to the partial coherence is continuous and the critical threshold is now larger compared to the deterministic case (T = 0). We derive an exact formula for the critical transition from incoherent to coherent oscillations for the deterministic and stochastic case based on both... (More)
We investigate the collective dynamics of a population of X Y model-type oscillators, globally coupled via non-separable interactions that are randomly chosen from a positive or negative value and subject to thermal noise controlled by temperature T. We find that the system at T = 0 exhibits a discontinuous, first-order like phase transition from the incoherent to the fully coherent state; when thermal noise is present (T > 0), the transition from incoherence to the partial coherence is continuous and the critical threshold is now larger compared to the deterministic case (T = 0). We derive an exact formula for the critical transition from incoherent to coherent oscillations for the deterministic and stochastic case based on both stability analysis for finite oscillators as well as for the thermodynamic limit (N → ∞) based on a rigorous mean-field theory using graphons, valid for heterogeneous graph structures. Our theoretical results are supported by extensive numerical simulations. Remarkably, the synchronization threshold induced by the type of random coupling considered here is identical to the one found in studies, which consider uniform input or output strengths for each oscillator node [H. Hong and S. H. Strogatz, Phys. Rev. E 84(4), 046202 (2011); Phys. Rev. Lett. 106(5), 054102 (2011)], which suggests that these systems display a "universal"character for the onset of synchronization.
The phenomena of magnetization and synchronization occurring in spin
(Less)
models and coupled oscillator models, respectively, are traditionally
regarded as completely separate and were, therefore, mostly studied
independently. However, the two models share collective behaviors
induced by the interacting units present in the system. Various
collective behaviors can be observed depending on the interaction type,
such as “glassy behavior,” where spins become “frustrated” when the
interaction among spins is chosen randomly from either positive or
negative values. The equations of motion for the spin models are known
as the 𝑋𝑌
model and can be related to a variant of the Kuramoto model of coupled
oscillators, an observation that motivates the present study. We
considered interactions (coupling strengths) drawn randomly from either a
fixed positive or negative value and studied the resulting collective
dynamics of the system using numerical simulations. We find that for the
deterministic case, when noise is absent, the system shows features of a
discontinuous, first-order like phase transition between incoherent and
perfectly coherent oscillations; for the noisy case, on the other hand,
this transition is found to be continuous. We explain and analyze this
phase transition using simple energetic arguments, linear stability
analysis, and a recently developed mean-field theory based on
graphons/graphops.
- author
- Hong, Hyunsuk
and Martens, Erik A.
LU
- organization
- publishing date
- 2022-06-01
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- dynamical system, Synchronization, oscillation, oscillator glass
- in
- Chaos
- volume
- 32
- issue
- 6
- article number
- 063125
- publisher
- American Institute of Physics (AIP)
- external identifiers
-
- scopus:85132282316
- pmid:35778126
- ISSN
- 1054-1500
- DOI
- 10.1063/5.0078431
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2022 Author(s).
- id
- 4bad67f7-c132-4c54-b32a-175ad53640c3
- date added to LUP
- 2022-07-12 15:00:42
- date last changed
- 2024-06-25 15:46:45
@article{4bad67f7-c132-4c54-b32a-175ad53640c3,
abstract = {{<p>We investigate the collective dynamics of a population of X Y model-type oscillators, globally coupled via non-separable interactions that are randomly chosen from a positive or negative value and subject to thermal noise controlled by temperature T. We find that the system at T = 0 exhibits a discontinuous, first-order like phase transition from the incoherent to the fully coherent state; when thermal noise is present (T > 0), the transition from incoherence to the partial coherence is continuous and the critical threshold is now larger compared to the deterministic case (T = 0). We derive an exact formula for the critical transition from incoherent to coherent oscillations for the deterministic and stochastic case based on both stability analysis for finite oscillators as well as for the thermodynamic limit (N → ∞) based on a rigorous mean-field theory using graphons, valid for heterogeneous graph structures. Our theoretical results are supported by extensive numerical simulations. Remarkably, the synchronization threshold induced by the type of random coupling considered here is identical to the one found in studies, which consider uniform input or output strengths for each oscillator node [H. Hong and S. H. Strogatz, Phys. Rev. E 84(4), 046202 (2011); Phys. Rev. Lett. 106(5), 054102 (2011)], which suggests that these systems display a "universal"character for the onset of synchronization. <br/></p><p>The phenomena of magnetization and synchronization occurring in spin <br>
models and coupled oscillator models, respectively, are traditionally <br>
regarded as completely separate and were, therefore, mostly studied <br>
independently. However, the two models share collective behaviors <br>
induced by the interacting units present in the system. Various <br>
collective behaviors can be observed depending on the interaction type, <br>
such as “glassy behavior,” where spins become “frustrated” when the <br>
interaction among spins is chosen randomly from either positive or <br>
negative values. The equations of motion for the spin models are known <br>
as the 𝑋𝑌<br>
model and can be related to a variant of the Kuramoto model of coupled <br>
oscillators, an observation that motivates the present study. We <br>
considered interactions (coupling strengths) drawn randomly from either a<br>
fixed positive or negative value and studied the resulting collective <br>
dynamics of the system using numerical simulations. We find that for the<br>
deterministic case, when noise is absent, the system shows features of a<br>
discontinuous, first-order like phase transition between incoherent and<br>
perfectly coherent oscillations; for the noisy case, on the other hand,<br>
this transition is found to be continuous. We explain and analyze this <br>
phase transition using simple energetic arguments, linear stability <br>
analysis, and a recently developed mean-field theory based on <br>
graphons/graphops.<sup/></p>}},
author = {{Hong, Hyunsuk and Martens, Erik A.}},
issn = {{1054-1500}},
keywords = {{dynamical system; Synchronization; oscillation; oscillator glass}},
language = {{eng}},
month = {{06}},
number = {{6}},
publisher = {{American Institute of Physics (AIP)}},
series = {{Chaos}},
title = {{First-order like phase transition induced by quenched coupling disorder}},
url = {{http://dx.doi.org/10.1063/5.0078431}},
doi = {{10.1063/5.0078431}},
volume = {{32}},
year = {{2022}},
}