Models with short- and long-range interactions: the phase diagram and the reentrant phase

Dauxois, Thierry; Buyl, Pierre de; Lori, Leonardo; Ruffo, Stefano

doi:10.1088/1742-5468/2010/06/p06015

Cited by 22 publications

(24 citation statements)

References 30 publications

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“…In this case, it may be easily checked that the eigenvalues of T are given by 2πI m (βK) with the corresponding eigenvector given by plane waves exp(iqθ)/ √ 2π [14]. Using I 0 (x) > I 1 (x) > I 2 (x) .…”

Section: J =mentioning

confidence: 99%

Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions

Gupta

Ruffo

2017

Entropy

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Abstract:We investigate the stationary and dynamic properties of the celebrated Nosé-Hoover dynamics of many-body interacting Hamiltonian systems, with an emphasis on the effect of inter-particle interactions. To this end, we consider a model system with both short-and long-range interactions. The Nosé-Hoover dynamics aim to generate the canonical equilibrium distribution of a system at a desired temperature by employing a set of time-reversible, deterministic equations of motion. A signature of canonical equilibrium is a single-particle momentum distribution that is Gaussian. We find that the equilibrium properties of the system within the Nosé-Hoover dynamics coincides with that within the canonical ensemble. Moreover, starting from out-of-equilibrium initial conditions, the average kinetic energy of the system relaxes to its target value over a size-independent timescale. However, quite surprisingly, our results indicate that under the same conditions and with only long-range interactions present in the system, the momentum distribution relaxes to its Gaussian form in equilibrium over a scale that diverges with the system size. On adding short-range interactions, the relaxation is found to occur over a timescale that has a much weaker dependence on system size. This system-size dependence of the timescale vanishes when only short-range interactions are present in the system. An implication of such an ultra-slow relaxation when only long-range interactions are present in the system is that macroscopic observables other than the average kinetic energy when estimated in the Nosé-Hoover dynamics may take an unusually long time to relax to its canonical equilibrium value. Our work underlines the crucial role that interactions play in deciding the equivalence between Nosé-Hoover and canonical equilibrium.

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Section: J =mentioning

confidence: 99%

Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions

Gupta

Ruffo

2017

Entropy

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“…In the present work, we are interested in the study of the dynamics of mixed systems, i. e. systems with a longrange potential but also with a strong core interaction at short distances. Previous works on this include the Ising model with neighbor interactions [33][34][35] and the HMF model modified by adding a short-range term [36][37][38]. In both cases, the results obtained are similar to the strict long-range case.…”

Section: Introductionmentioning

confidence: 56%

Hard-core collisional dynamics in Hamiltonian mean-field model

Melo

Figueiredo

Filho

et al. 2020

Communications in Nonlinear Science and Numerical Simulation

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We consider a modification of the well studied Hamiltonian Mean-Field model by introducing a hard-core point-like repulsive interaction and propose a numerical integration scheme to integrate numerically its dynamics. Our results show that the outcome of the initial violent relaxation is altered, and also that the phase-diagram is modified with a critical temperature at a higher value than in the non-collisional counterpart.

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“…This is a typical 'reentrant ' behaviour. Reentrant phenomena of this type are common in statistical systems, whenever competing interactions are present [22][23][24][25]. For a fixed ρ Λ , for R < R A metastable states do exist and for R A < R < R IA no thermodynamic equilibria exist.…”

Section: Resultsmentioning

confidence: 99%

Gravothermal catastrophe with a cosmological constant

2012

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We investigate the effect of a cosmological constant on the gravothermal catastrophe in the Newtonian limit. A negative cosmological constant acts as a thermodynamic 'destabilizer'. The Antonov radius gets smaller and the instability occurs, not only for negative but also for positive energy values. A positive cosmological constant acts as a 'stabilizer' of the system, which, in this case, exhibits a novel 'reentrant behaviour'. In addition to the Antonov radius we find a second critical radius, where an 'inverse Antonov transition' occurs; a series of local entropy maxima is restored.

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Models with short- and long-range interactions: the phase diagram and the reentrant phase

Cited by 22 publications

References 30 publications

Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions

Equilibration in the Nosé–Hoover Isokinetic Ensemble: Effect of Inter-Particle Interactions

Hard-core collisional dynamics in Hamiltonian mean-field model

Gravothermal catastrophe with a cosmological constant

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