Phase-Separation Kinetics in the Two-Dimensional Long-Range Ising Model

Müller, Fabio; Christiansen, Henrik; Janke, Wolfhard

doi:10.1103/physrevlett.129.240601

Cited by 9 publications

(4 citation statements)

References 60 publications

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“…For a recently developed much faster but more involved hierarchical and adaptive tree-like single-spin update algorithm that is compatible with O(log N ) complexity, see Refs. [22,23].…”

Section: Model and Methodsmentioning

confidence: 99%

The role of magnetization in phase-ordering kinetics of the short-range and long-range Ising model

Janke

Christiansen

Majumder

2023

Eur. Phys. J. Spec. Top.

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The kinetics of phase ordering has been investigated for numerous systems via the growth of the characteristic length scale $$\ell (t) \sim t^{\alpha }$$ ℓ ( t ) ∼ t α quantifying the size of ordered domains as a function of time t, where $$\alpha$$ α is the growth exponent. The behavior of the squared magnetization $$\langle m(t)^{2}\rangle$$ ⟨ m ( t ) 2 ⟩ has mostly been ignored, even though it is one of the most fundamental observables for spin systems. This is most likely due to its vanishing for quenches in the thermodynamic limit. For finite systems, on the other hand, we show that the squared magnetization does not vanish and may be used as an easier to extract alternative to the characteristic length. In particular, using analytical arguments and numerical simulations, we show that for quenches into the ordered phase, one finds $$\langle m(t)^{2} \rangle \sim m_0^2 t^{d\alpha }/V,$$ ⟨ m ( t ) 2 ⟩ ∼ m 0 2 t d α / V , where $$m_0$$ m 0 is the equilibrium magnetization, d the spatial dimension, and V the volume of the system.

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“…For a recently developed much faster but more involved hierarchical and adaptive tree-like single-spin update algorithm that is compatible with O(log N ) complexity, see Refs. [22,23].…”

Section: Model and Methodsmentioning

confidence: 99%

The role of magnetization in phase-ordering kinetics of the short-range and long-range Ising model

Janke

Christiansen

Majumder

2023

Eur. Phys. J. Spec. Top.

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“…[34] A first concrete application to the coarsening kinetics of the conserved Ising model has just appeared. [35] Our new method for polymers [33] allows efficient simulations of the collapse transition of polymers with untruncated Lennard-Jones interactions. [36] As will be discussed below, it also gives completely new possibilities for investigating seemingly simple (athermal) hard-sphere polymers and enables novel observations which would have been hardly possible with standard simulation techniques.…”

Section: Doi: 101002/mats202200080mentioning

confidence: 99%

“…[ 34 ] A first concrete application to the coarsening kinetics of the conserved Ising model has just appeared. [ 35 ]…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Simulation of Long Hard‐Sphere Polymer Chains in Two to Five Dimensions

Schnabel

Janke

2023

Macro Theory & Simulations

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Simulations are performed for long hard‐sphere polymer chains using a recently developed binary‐tree based Monte Carlo method. Systems in two to five dimensions with free and periodic boundary conditions and up to 107 repeat units are considered. The analysis is focused on scaling properties of the end‐to‐end distance and the entropy and their dependence on the sphere diameter. To this end new methods for measuring entropy and its derivatives are introduced. By determining the Flory exponent ν and the weakly universal amplitude ratio of end‐to‐end distance to radius of gyration we find that the system generally reproduces the behavior of self‐avoiding lattice walks in strong support of universality.

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“…Subsequently, the general setup of the method inspired another "external" variant that can deal very efficiently with algebraically decaying long-range interactions of particle and spin systems [34]. A first concrete application to the coarsening kinetics of the conserved Ising model has just appeared [35].…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions

Schnabel¹,

Janke²

2023

Preprint

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Phase-Separation Kinetics in the Two-Dimensional Long-Range Ising Model

Cited by 9 publications

References 60 publications

The role of magnetization in phase-ordering kinetics of the short-range and long-range Ising model

The role of magnetization in phase-ordering kinetics of the short-range and long-range Ising model

Monte Carlo Simulation of Long Hard‐Sphere Polymer Chains in Two to Five Dimensions

Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions

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