Dipolar needles in the microcanonical ensemble: Evidence of spontaneous magnetization and ergodicity breaking

Miloshevich, George; Dauxois, Thierry; Khomeriki, Ramaz; Ruffo, Stefano

doi:10.1209/0295-5075/104/17011

Cited by 34 publications

(19 citation statements)

References 25 publications

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“…In agreement with Ref. [12], we see the coexistence of antiferromagnetic and magnetic states in a tiny range of energy per spin [ -2.135 , -2.125 ] if the aspect ratio of the system is quite large. In particular, in order to realise a robust ferromagnetic state one should take at least a 2 × 2 × 32 dipolar system.…”

Section: Arxiv:200103748v2 [Cond-matstat-mech] 19 Feb 2020supporting

confidence: 92%

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Effective negative specific heat by destabilization of metastable states in dipolar systems

et al. 2020

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We study dipolarly coupled three dimensional spin systems in both the microcanonical and the canonical ensembles by introducing appropriate numerical methods to determine the microcanonical temperature and by realizing a canonical model of heat bath. In the microcanonical ensemble, we show the existence of a branch of stable antiferromagnetic states in the low energy region. Other metastable ferromagnetic states exist in this region: by externally perturbing them, an effective negative specific heat is obtained. In the canonical ensemble, for low temperatures, the same metastable states are unstable and reach a new branch of more robust metastable states which is distinct from the stable one. Our statistical physics approach allows us to put some order in the complex structure of stable and metastable states of dipolar systems.

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Section: Arxiv:200103748v2 [Cond-matstat-mech] 19 Feb 2020supporting

confidence: 92%

“…However, it has been argued in Ref. [12] that, in the thermodynamic limit [13], the ferromagnetic state survives only in the case of a body-centered cubic lattice. Despite this fact, we show in the present paper that, when considering a finite simple cubic lattice with 2×2 base and a large aspect ratio ergodicity breaking and negative specific heat are found.…”

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confidence: 99%

Effective negative specific heat by destabilization of metastable states in dipolar systems

et al. 2020

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“…We have proved a Lieb-Robinson-type result, providing an upper bound on u AB (t) in (2) [and hence on the Poisson bracket (1)] for a broad class of classical long-range interacting lattice models in arbitrary spatial dimension. Dipolar interactions in condensed matter systems are the prime example of such long-range interacting lattice systems [16], but many other examples exist [17]. To avoid the rather technical notation of the general result [18], we present the main result in this Letter for a specific class of systems, namely classical XY models in d spatial dimensions with pair interactions that decay like a power law 1/|i − j| α with the (1-norm) distance |i − j| between lattice sites i and j.…”

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Spreading of Perturbations in Long-Range Interacting Classical Lattice Models

2014

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Lieb-Robinson-type bounds are reported for a large class of classical Hamiltonian lattice models. By a suitable rescaling of energy or time, such bounds can be constructed for interactions of arbitrarily long range. The bound quantifies the dependence of the system's dynamics on a perturbation of the initial state. The effect of the perturbation is found to be effectively restricted to the interior of a causal region of logarithmic shape, with only small, algebraically decaying effects in the exterior. A refined bound, sharper than conventional Lieb-Robinson bounds, is required to correctly capture the shape of the causal region, as confirmed by numerical results for classical long-range XY chains. We discuss the relevance of our findings for the relaxation to equilibrium of long-range interacting lattice models.In many nonrelativistic lattice systems, and despite the absence of Lorentz covariance, physical effects are mostly restricted to a causal region, often in the shape of an effective "light cone," with only tiny effects leaking out to the exterior. The technical tool, known as the LiebRobinson bound [1,2], to quantify this statement in a quantum mechanical context is an upper bound on the norm of the commutator ½O A ðtÞ; O B ð0Þ, where O A ð0Þ and O B ð0Þ are operators supported on the subspaces of the Hilbert space corresponding to nonoverlapping regions A and B of the lattice. The importance of such a bound lies in the fact that a multitude of physically relevant results can be derived from it. Examples are bounds on the creation of equal-time correlations [3], on the transmission of information [4], and on the growth of entanglement [5], the exponential spatial decay of correlations in the ground state of a gapped system [6], or a Lieb-Schultz-Mattis theorem in higher dimensions [7]. Experimental observations related to Lieb-Robinson bounds have also been reported [8].The original proof by Lieb and Robinson [1] requires interactions of finite range. An extension to power-lawdecaying long-range interactions has been reported in Refs. [3,6]. In this case the effective causal region is no longer cone shaped, and the spatial propagation of physical effects is not limited by a finite group velocity [9]. For "strong long-range interactions," i.e., when the interaction potential decays proportionally to 1=r α with an exponent α smaller than the lattice dimension d, the theorems in [3,6] do not apply and no Lieb-Robinson-type results are known. This fact nicely fits into the larger picture that, for α ≤ d, the behavior of long-range interacting systems often differs substantially from that of short-range interacting systems. Examples of such differences include nonequivalent equilibrium statistical ensembles and negative response functions [10], or the occurrence of quasistationary states whose lifetimes diverge with the system size [11,12]. The latter is a dynamical phenomenon, and it has been conjectured in [13] that some of its properties are universal and in some way connected to Lieb-Robinson bounds.In mos...

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“…Broken ergodicity is observed in many other physical systems including classical dipolar spin systems. 73 It is most suitable to consider a pseudo-spectral code 41 to investigate whether the relaxation of the Fourier modes in MHD can occur. The advantages of using Galerkin methods in general involve accuracy and "semiconservation" of the integrals of motion.…”

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confidence: 99%

Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales

2018

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The direction of cascades in a two-dimensional model that takes electron inertia and ion sound Larmor radius into account is studied, resulting in analytical expressions for the absolute equilibrium states of the energy and helicities. These states suggest that typically both the energy and magnetic helicity at scales shorter than electron skin depth have direct cascade, while at large scales the helicity has an inverse cascade as established earlier for reduced magnetohydrodynamics (MHD). The calculations imply that the introduction of gyro-effects allows for the existence of negative temperature (conjugate to energy) states and the condensation of energy to the large scales. Comparisons between twoand three-dimensional extended MHD models (MHD with two-fluid effects) show qualitative agreement between the two.

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Dipolar needles in the microcanonical ensemble: Evidence of spontaneous magnetization and ergodicity breaking

Cited by 34 publications

References 25 publications

Effective negative specific heat by destabilization of metastable states in dipolar systems

Effective negative specific heat by destabilization of metastable states in dipolar systems

Spreading of Perturbations in Long-Range Interacting Classical Lattice Models

Direction of cascades in a magnetofluid model with electron skin depth and ion sound Larmor radius scales

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