Phase diagram for a zero-temperature Glauber dynamics under partially synchronous updates

Skorupa, Bartosz; Sznajd-Weron, Katarzyna; Topolnicki, Rafał

doi:10.1103/physreve.86.051113

Cited by 7 publications

(7 citation statements)

References 31 publications

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“…2. Such a modification reminds of the generalized zero-temperature Glauber dynamics introduced in [15], which occurred to be particularly interesting from theo-retical point of view [23,[25][26][27]32]. As we will see, the above dynamics, although artificial and not motivated by any physical processes, will also turn out to be particularly intriguing.…”

Section: Different Dynamicsmentioning

confidence: 73%

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Kinetic Ising models with various single-spin-flip dynamics on quenched and annealed random regular graphs

2017

Self Cite

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We investigate a kinetic Ising model with several single-spin flip dynamics (including Metropolis and heat-bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the same results since the conditions for the detailed balance and the Boltzmann distribution in an equilibrium are satisfied. However, on the annealed graphs situation is far less clear -the network annealing disturbs the equilibrium moving the system away from it. Consequently, distinct dynamics lead to different steady states. We show that some algorithms are more resistant to the annealed disorder, which causes only small quantitative changes in the model behavior. On the other hand, there are dynamics for which the influence of annealing on the system is significant, and qualitative changes arise like switching the type of phase transition from continuous to discontinuous one. We try to identify features of the proposed dynamics which are responsible for the above phenomenon.

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Section: Different Dynamicsmentioning

confidence: 73%

“…Ising model, although already 100 years old still inspires many researchers and raises new questions [25][26][27][28][29][30]32]. Recently we have introduced, under the name the q-neighbor Ising model, a seemingly small modification of the kinetic Ising model with Metropolis dynamics allowing each spin to interact only with q neighbors [1].…”

Section: Discussionmentioning

confidence: 99%

Kinetic Ising models with various single-spin-flip dynamics on quenched and annealed random regular graphs

2017

Self Cite

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“…1a and 1b). For synchronous updates there is, however, also a periodic state where the opinions alternate in space [10]: if all odd sites are black and all even sites white at time t, all opinions are inverted at t + 1 and return to the original state at t + 2 ( Fig. 1c).…”

Section: Motivation: Stochastic Synchronous Voter Modelmentioning

confidence: 99%

The Ising chain constrained to an even or odd number of positive spins

Gastner¹

2015

J. Stat. Mech.

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Abstract. We investigate the statistical mechanics of the periodic one-dimensional Ising chain when the number of positive spins is constrained to be either an even or an odd number. We calculate the partition function using a generalization of the transfer matrix method. On this basis, we derive the exact magnetization, susceptibility, internal energy, heat capacity and correlation function. We show that in general the constraints substantially slow down convergence to the thermodynamic limit. By taking the thermodynamic limit together with the limit of zero temperature and zero magnetic field, the constraints lead to new scaling functions and different probability distributions for the magnetization. We demonstrate how these results solve a stochastic version of the one-dimensional voter model.

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“…The final state of quenching the nearest-neighbor Ising model to zero-temperature depends on the spatial dimensionality of the system. In one-dimension the ground state is always reached [12], while in three-dimensions the final states are a host of topologically complex configurations that are forever trapped at constant energy in a local minima [13][14][15]. In two-dimensions, one finds not only the ground state, but also "frozen" on-axis stripe states, or long-lived off-axis stripe evolutions [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Universal behavior in finite 2D kinetic ferromagnets

Denholm¹,

Hourahine²

2018

Preprint

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We study the time evolution of the two-dimensional kinetic Ising model in finite systems with a non-conserved order parameter, considering nearest-neighbour interactions on the square lattice with periodic and open boundary conditions. Universal data collapse in spin product correlation functions is observed which, when expressed in rescaled units, is valid across the entire time evolution of the system at all length scales, not just within the time regime usually considered in the dynamical scaling hypothesis. Consequently, beyond rapidly decaying finite size effects, the evolution of correlations in small finite systems parallels arbitrarily larger cases, even at large fractions of the size of these finite systems.

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Phase diagram for a zero-temperature Glauber dynamics under partially synchronous updates

Cited by 7 publications

References 31 publications

Kinetic Ising models with various single-spin-flip dynamics on quenched and annealed random regular graphs

Kinetic Ising models with various single-spin-flip dynamics on quenched and annealed random regular graphs

The Ising chain constrained to an even or odd number of positive spins

Universal behavior in finite 2D kinetic ferromagnets

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