Stochastic Kuramoto oscillators with discrete phase states

Jörg, David J.

doi:10.1103/physreve.96.032201

Cited by 10 publications

(14 citation statements)

References 54 publications

(155 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Until recently it was widely believed that the J ij = ±1 system does not harbor spin-glass order (unlike the model with normal-distributed couplings), only power-law decaying critical EA spin-spin correlations [30][31][32]. More recent studies [22,33,34] point to significant long-range order. In particular, Thomas et al [22] evaluated the Pfaffian form of the partition function on larger lattices and lower temperatures than in previous MC studies.…”

Section: Model and Methodsmentioning

confidence: 99%

Dual time scales in simulated annealing of a two-dimensional Ising spin glass

Rubin

Sandvik

2017

Phys. Rev. E

View full text Add to dashboard Cite

We apply a generalized Kibble-Zurek out-of-equilibrium scaling ansatz to simulated annealing when approaching the spin-glass transition at temperature T=0 of the two-dimensional Ising model with random J=±1 couplings. Analyzing the spin-glass order parameter and the excess energy as functions of the system size and the annealing velocity in Monte Carlo simulations with Metropolis dynamics, we find scaling where the energy relaxes slower than the spin-glass order parameter, i.e., there are two different dynamic exponents. The values of the exponents relating the relaxation time scales to the system length, τ∼L^{z}, are z=8.28±0.03 for the relaxation of the order parameter and z=10.31±0.04 for the energy relaxation. We argue that the behavior with dual time scales arises as a consequence of the entropy-driven ordering mechanism within droplet theory. We point out that the dynamic exponents found here for T→0 simulated annealing are different from the temperature-dependent equilibrium dynamic exponent z_{eq}(T), for which previous studies have found a divergent behavior: z_{eq}(T→0)→∞. Thus, our study shows that, within Metropolis dynamics, it is easier to relax the system to one of its degenerate ground states than to migrate at low temperatures between regions of the configuration space surrounding different ground states. In a more general context of optimization, our study provides an example of robust dense-region solutions for which the excess energy (the conventional cost function) may not be the best measure of success.

show abstract

Section: Model and Methodsmentioning

confidence: 99%

Dual time scales in simulated annealing of a two-dimensional Ising spin glass

Rubin

Sandvik

2017

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…To achieve temporal and spatial coherence as well as high precision, cell-autonomous oscillators are typically coupled [19,37,38]. Such coupling facilitates synchronization and can affect the collective frequency [39][40][41][42][43][44][45][46][47]. Moreover, coupling between cellular oscillators via paracrine or juxtacrine signaling (i.e., via diffusible signals or contact-dependent signaling) typically proceeds at time scales similar to the oscillation period, implying the presence of coupling delays that can have profound effects on the coupled dynamics [21,[40][41][42]48].…”

Section: Introductionmentioning

confidence: 99%

Chemical event chain model of coupled genetic oscillators

2018

Self Cite

View full text Add to dashboard Cite

We introduce a stochastic model of coupled genetic oscillators in which chains of chemical events involved in gene regulation and expression are represented as sequences of Poisson processes. We characterize steady states by their frequency, their quality factor, and their synchrony by the oscillator cross correlation. The steady state is determined by coupling and exhibits stochastic transitions between different modes. The interplay of stochasticity and nonlinearity leads to isolated regions in parameter space in which the coupled system works best as a biological pacemaker. Key features of the stochastic oscillations can be captured by an effective model for phase oscillators that are coupled by signals with distributed delays.

show abstract

“…For the Gaussian case, where the interaction distribution is continuous and the ground state is unique, there is now also general consensus concerning the low temperature thermodynamic limit (ThL) behavior and exponents. In the bimodal case there is an "effectively continuous energy level distribution" regime coming down from high temperatures and ending with a crossover at a size dependent temperature T * (L) to a ground state dominated regime [3]. Interpretations differ considerably concerning the critical exponents for the bimodal interaction case.…”

Section: Introductionmentioning

confidence: 99%

Bimodal and Gaussian Ising spin glasses in dimension two

Lundow

Campbell

2016

Phys. Rev. E

View full text Add to dashboard Cite

An analysis is given of numerical simulation data to size L=128 on the archetype square lattice Ising spin glasses (ISGs) with bimodal (±J) and Gaussian interaction distributions. It is well established that the ordering temperature of both models is zero. The Gaussian model has a nondegenerate ground state and thus a critical exponent η≡0, and a continuous distribution of energy levels. For the bimodal model, above a size-dependent crossover temperature T(*)(L) there is a regime of effectively continuous energy levels; below T(*)(L) there is a distinct regime dominated by the highly degenerate ground state plus an energy gap to the excited states. T(*)(L) tends to zero at very large L, leaving only the effectively continuous regime in the thermodynamic limit. The simulation data on both models are analyzed with the conventional scaling variable t=T and with a scaling variable τ(b)=T(2)/(1+T(2)) suitable for zero-temperature transition ISGs, together with appropriate scaling expressions. The data for the temperature dependence of the reduced susceptibility χ(τ(b),L) and second moment correlation length ξ(τ(b),L) in the thermodynamic limit regime are extrapolated to the τ(b)=0 critical limit. The Gaussian critical exponent estimates from the simulations, η=0 and ν=3.55(5), are in full agreement with the well-established values in the literature. The bimodal critical exponents, estimated from the thermodynamic limit regime analyses using the same extrapolation protocols as for the Gaussian model, are η=0.20(2) and ν=4.8(3), distinctly different from the Gaussian critical exponents.

show abstract

Stochastic Kuramoto oscillators with discrete phase states

Cited by 10 publications

References 54 publications

Dual time scales in simulated annealing of a two-dimensional Ising spin glass

Dual time scales in simulated annealing of a two-dimensional Ising spin glass

Chemical event chain model of coupled genetic oscillators

Bimodal and Gaussian Ising spin glasses in dimension two

Contact Info

Product

Resources

About