Collective oscillations in a three-dimensional spin model with non-reciprocal interactions (2405.13925v1)
Abstract: We study the onset of collective oscillations at low temperature in a three-dimensional spin model with non-reciprocal short-range interactions. Performing numerical simulations of the model, the presence of a continuous phase transition to global oscillations is confirmed by a finite-size scaling analysis. By systematically varying the interaction range, we show that collective oscillations in this spin model actually result from two successive phase transitions: a mean-field phase transition over finite-size neighborhoods, which leads to the emergence of local noisy oscillators, and a synchronization transition of local noisy oscillators, which generates coherent macroscopic oscillations. Using a Fokker-Planck equation under a local mean-field approximation, we derive from the spin dynamics coupled Langevin equations for the complex amplitudes describing noisy oscillations on a mesoscopic scale. The phase diagram of these coupled equations is qualitatively obtained from a fully-connected (mean-field) approximation. This analytical approach allows us to clearly disentangle the onset of local and global oscillations, and to identify the two main control parameters, expressed as combinations of the microscopic parameters of the spin dynamics, that control the phase diagram of the model.
- G. Nicolis. Dissipative systems. Rep. Prog. Phys. 49, 873 (1986).
- The Kuramoto model: A simple paradigm for synchronization phenomena. Rev. Mod. Phys. 77, 137 (2005).
- Kuramoto model of synchronization: equilibrium and nonequilibrium aspects. J. Stat. Mech.: Theor. Exp. page R08001 (2014).
- The free-energy cost of accurate biochemical oscillations. Nat. Phys. 11, 772 (2015).
- Phase transition in thermodynamically consistent biochemical oscillators. J. Chem. Phys. 149, 045101 (2018).
- Complex dynamics in a synchronized cell-free genetic clock. Nat. Commun. 13, 2852 (2022).
- Phase-transition oscillations induced by a strongly focused laser beam. Phys. Rev. E 92, 052312 (2015).
- Rhythmic behavior in a two-population mean-field Ising model. Phys. Rev. E. 94, 042139 (2016).
- D. De Martino and A. C. Barato. Oscillations in feedback driven systems: thermodynamics and noise. Phys. Rev. E 100, 062123 (2019).
- Oscillatory behavior in a model of non-Markovian mean-field interacting spins. J. Stat. Phys. 179, 690 (2020).
- Emergence of collective self-oscillations in minimal lattice models with feedback. Phys. Rev. E 108, 044204 (2023).
- Endogenous Crisis Waves: Stochastic Model with Synchronized Collective Behavior. Phys. Rev. Lett. 114, 088701 (2015).
- Symmetry restoration by pricing in a duopoly of perishable goods. J. Stat. Mech.: Theor. Exp. page P11001 (2015).
- Entropy Production of Cyclic Population Dynamics. Phys. Rev. Lett. 104, 218102 (2010).
- Hopf-Hopf bifurcation and chaotic attractors in a delayed diffusive predator-prey model with fear effect. Chaos, Solitons and Fractals 123, 206 (2019).
- J. D. Crawford. Introduction to bifurcation theory. Rev. Mod. Phys. 63, 991 (1991).
- Design principles for enhancing phase sensitivity and suppressing phase fluctuations simultaneously in biochemical oscillatory systems. Nat. Commun. 9, 1434 (2018).
- P. Gaspard. The correlation time of mesoscopic chemical clocks. J. Chem. Phys. 117, 8905 (2002).
- A. C. Barato and U. Seifert. Cost and precision of Brownian clocks. Phys. Rev. X 6, 041053 (2016).
- A. C. Barato and U. Seifert. Coherence of biochemical oscillations is bounded by driving force and network topology. Phys. Rev. E 95, 062409 (2017).
- Universal minimal cost of coherent biochemical oscillations. Phys. Rev. E 106, 014106 (2022).
- Coherence of oscillations in the weak-noise limit. Phys. Rev. E 105, 064101 (2022).
- Spatiotemporal order out of noise. Rev. Mod. Phys. 79, 829 (2007).
- Langevin approach for intrinsic fluctuations of chemical reactions with Hopf bifurcation. Physica D 411, 132612 (2020).
- L. Guislain and E. Bertin. Non-equilibrium phase transition to temporal oscillations in mean-field spin models. Phys. Rev. Lett. 130, 207102 (2023).
- L. Guislain and E. Bertin. Discontinuous Phase Transition from Ferromagnetic to Oscillating States in a Nonequilibrium Mean-Field Spin Model. Phys. Rev. E 109, 034131 (2024).
- L. Crochik and T. Tomé. Entropy production in the majority-vote model. Phys. Rev. E 72, 057103 (2005).
- Entropy production and fluctuation theorem along a stochastic limit cycle. J. Chem. Phys. 129, 114506 (2008).
- Stochastic Thermodynamics in Mesoscopic Chemical Oscillation Systems. J. Phys. Chem. B 113, 9316 (2009).
- A. C. Barato and H. Hinrichsen. Entropy production of a bound nonequilibrium interface. J. Phys. A: Math. Theor. 45, 115005 (2012).
- T. Tomé and M. J. de Oliveira. Entropy production in nonequilibrium systems at stationary states. Phys. Rev. Lett. 108, 020601 (2012).
- Entropy production as tool for characterizing nonequilibrium phase transitions. Phys. Rev. E 100, 012104 (2019).
- Entropy production at criticality in a nonequilibrium Potts model. New J. Phys. 22, 093069 (2020).
- Irreversibility in dynamical phases and transitions. Nat. Commun. 12, 392 (2021).
- Confinement-Induced Transition between Wavelike Collective Cell Migration Modes. Phys. Rev. Lett. 122, 168101 (2019).
- Sustained Oscillations of Epithelial Cell Sheets. Biophysical Journal 117, 464 (2019).
- Fold-change detection and scale invariance of cell–cell signaling in social amoeba. Proc. Natl. Acad. Sci. USA 114, E4149 (2017).
- Emergence of collective oscillations in adaptive cells. Nat. Commun. 10, 5613 (2019).
- Scalar active mixture: The nonreciprocal Cahn-Hilliard model. Phys. Rev. X 10, 041009 (2020).
- Nonreciprocity as a generic route to traveling states. Proc. Natl. Acad. Sci. USA 117, 19767 (2020).
- The transition to collective motion in nonreciprocal active matter: coarse graining agent-based models into fluctuating hydrodynamics. (2024). Preprint arXiv:2307.08251.
- Universal Critical Behavior of Noisy Coupled Oscillators. Phys. Rev. Lett. 93, 175702 (2004).
- Universal Critical Behavior of Noisy Coupled Oscillators: A Renormalization Group Study. Phys. Rev. E 72, 016130 (2005).
- The Non-Reciprocal Ising Model. (2023). Preprint arxiv:2311.05471.
- V. Privman. Finite Size Scaling and Numerical Simulation of Statistical Systems. WORLD SCIENTIFIC 1990.
- Scaling Theory for Finite-Size Effects in the Critical Region. Phys. Rev. Lett. 28, 1516 (1972).
- A. P. Gottlob and M. Hasenbusch. Critical Behaviour of the 3D XY-model: A Monte Carlo Study. Physica A 201, 593 (1993).
- K. Huang. Statistical Mechanis, 2nd Ed. Wiley India Pvt. Limited 2008.
- Universality of Synchrony: Critical Behavior in a Discrete Model of Stochastic Phase-Coupled Oscillators. Phys. Rev. Lett. 96, 145701 (2006).
- Critical Behavior and Synchronization of Discrete Stochastic Phase-Coupled Oscillators. Phys. Rev. E 74, 031113 (2006).
- I. S. Aranson and L. Kramer. The world of the complex Ginzburg-Landau equation. Rev. Mod. Phys. 74, 99 (2002).