Publisher's Note: Topological nonconnectivity threshold in long-range spin systems [Phys. Rev. E<b>73</b>, 026116 (2006)]

Borgonovi, Fausto; Celardo, G. L.; Musesti, Alessandro; Trasarti-Battistoni, R.; Váchal, Pavel

doi:10.1103/physreve.73.039903

Cited by 9 publications

(21 citation statements)

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“…( m x , m y , m z ) = dθdφdp θ dp φ (sin θ cos φ, sin θ sin φ, cos θ)δf. (19) The linearized dynamics at long times is expected to be dominated by the mode corresponding to the largest eigenfrequency ω of the linearized equation (18), so that we may write…”

Section: Isotropic Heisenberg Mean-field Modelmentioning

confidence: 99%

Quasistationarity in a model of long-range interacting particles moving on a sphere

Gupta

Mukamel

2013

Phys. Rev. E

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We consider a long-range interacting system of N particles moving on a spherical surface under an attractive Heisenberg-like interaction of infinite range and evolving under deterministic Hamilton dynamics. The system may also be viewed as one of globally coupled Heisenberg spins. In equilibrium, the system has a continuous phase transition from a low-energy magnetized phase, in which the particles are clustered on the spherical surface, to a high-energy homogeneous phase. The dynamical behavior of the model is studied analytically by analyzing the Vlasov equation for the evolution of the single-particle distribution and numerically by direct simulations. The model is found to exhibit long-lived nonmagnetized quasistationary states (QSSs) which in the thermodynamic limit are dynamically stable within an energy range where the equilibrium state is magnetized. For finite N, these states relax to equilibrium over a time that increases algebraically with N. In the dynamically unstable regime, nonmagnetized states relax fast to equilibrium over a time that scales as lnN. These features are retained in presence of a global anisotropy in the magnetization.

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Section: Isotropic Heisenberg Mean-field Modelmentioning

confidence: 99%

Quasistationarity in a model of long-range interacting particles moving on a sphere

Gupta

Mukamel

2013

Phys. Rev. E

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“…Gaps may open up in the order parameters space. Such gaps have been recently reported in a class of anisotropic XY models [2,3] and for a discrete spin system [4]. Since the accessible region in the order parameters space is no more connected, ergodicity breaking naturally appears when a continuous microcanonical dynamics is considered.…”

Section: Introductionmentioning

confidence: 83%

Phase space gaps and ergodicity breaking in systems with long-range interactions

et al. 2008

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We study a generalized isotropic XY model which includes both two- and four-spin mean-field interactions. This model can be solved in the microcanonical ensemble. It is shown that in certain parameter regions the model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking. This phenomenon has previously been reported in anisotropic and discrete spin models. The entropy of the model is calculated and the microcanonical phase diagram is derived, showing the existence of first-order phase transitions from the ferromagnetic to a paramagnetic disordered phase. It is found that ergodicity breaking takes place in both the ferromagnetic and paramagnetic phases. As a consequence, the system can exhibit a stable ferromagnetic phase within the paramagnetic region, and conversely a disordered phase within the magnetically ordered region.

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“…Ergodicity breaking in models with long range interactions has recently been explicitly demonstrated in a number of models such as a class of anisotropic XY models [22,23], discrete spin Ising models [20], mean-field φ 4 models [24,25] and isotropic XY models with four-spin interactions [26]. Here we outline a demonstration of this feature for the Ising model with long and short range interactions defined in the previous section [20].…”

Section: Ergodicity Breakingmentioning

confidence: 89%

Statistical Mechanics of systems with long range interactions

Mukamel¹

2008

AIP Conference Proceedings

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Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d dimensions. As a result, these systems are non-additive and they display unusual thermodynamic and dynamical properties which are not present in systems with short range interactions. In particular, the various statistical mechanical ensembles are not equivalent and the microcanonical specific heat may be negative. Long range interactions may also result in breaking of ergodicity, making the maximal entropy state inaccessible from some regions of phase space. In addition, in many cases long range interactions result in slow relaxation processes, with time scales which diverge in the thermodynamic limit. Various models which have been found to exhibit these features are discussed.Comment: Published in AIP Conference Proceedings 970 "Dynamics and Thermodynamics of Systems with Long-Range Interactions: Theory and Experiments", Assisi, Italy 4-8 July 2007, editors A. Campa, A. Giansanti, G. Morigi and F. Sylos Labini, p. 22 (2008

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Publisher's Note: Topological nonconnectivity threshold in long-range spin systems [Phys. Rev. E73, 026116 (2006)]

Cited by 9 publications

References 0 publications

Quasistationarity in a model of long-range interacting particles moving on a sphere

Quasistationarity in a model of long-range interacting particles moving on a sphere

Phase space gaps and ergodicity breaking in systems with long-range interactions

Statistical Mechanics of systems with long range interactions

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