Critical dynamics of long-range models on dynamical Lévy lattices

R., Aiudi,; Burioni, Raffaella; Vezzani, A.

doi:10.1103/physrevb.107.224204

Phys. Rev. B

2023

DOI: 10.1103/physrevb.107.224204

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Critical dynamics of long-range models on dynamical Lévy lattices

Aiudi, R.

Raffaella Burioni

A. Vezzani

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2024

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Ordering kinetics with long-range interactions: interpolating between voter and Ising models

Corberi,

dello Russo,

Smaldone

2024

J. Stat. Mech.

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We study the ordering kinetics of a generalization of the voter model with long-range interactions, the p-voter model, in one dimension. It is defined in terms of Boolean variables S i , agents or spins, located on sites i of a lattice, each of which takes in an elementary move the state of the majority of p other agents at distances r chosen with probability P ( r ) ∝ r − α . For p = 2 the model can be exactly mapped onto the case with p = 1, which amounts to the voter model with long-range interactions decaying algebraically. For 3 ⩽ p < ∞ , instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant J ( r ) = P ( r ) quenched to small finite temperatures. In the limit p → ∞ , a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for p > 3 a closed set of differential equations cannot be found, we employed numerical simulations to address this case.

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Ordering kinetics with long-range interactions: interpolating between voter and Ising models

Corberi,

dello Russo,

Smaldone

2024

J. Stat. Mech.

View full text Add to dashboard Cite

show abstract

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Critical dynamics of long-range models on dynamical Lévy lattices

Cited by 1 publication

References 46 publications

Ordering kinetics with long-range interactions: interpolating between voter and Ising models

Ordering kinetics with long-range interactions: interpolating between voter and Ising models

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