Dynamical and stationary critical behavior of the Ising ferromagnet in a thermal gradient

Muglia, J.; Albano, Ezequiel V.

doi:10.1140/epjb/e2012-30051-1

Cited by 2 publications

(2 citation statements)

References 20 publications

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“…Very recently, the gradient method has been extended as a powerful tool to study first-and second-order irreversible phase transitions in far-from-equilibrium systems such as the Ziff-Gulari-Barshad model and forest-fire cellular automata [21,22]. In magnetic systems, damage spreading processes in a temperature gradient [23] and studies of several one-dimensional models [24,25,26,27] have been followed by the investigation of the kinetic Ising model in two dimensions under a variety of dynamics [28,29,30,31,32].…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium critical behavior of magnetic thin films grown in a temperature gradient

Candia¹,

Albano²

2012

J. Stat. Mech.

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We investigate the irreversible growth of (2 + 1)−dimensional magnetic thin films under the influence of a transverse temperature gradient, which is maintained by thermal baths across a direction perpendicular to the direction of growth. Therefore, different longitudinal layers grow at different temperatures between T 1 and T 2 , where T 1 < T hom c < T 2 and T hom c = 0.69(1) is the critical temperature of films grown in homogeneous thermal baths. We find a far-from-equilibrium continuous order-disorder phase transition driven by the thermal bath gradient. We characterize this gradient-induced critical behavior by means of standard finite-size scaling procedures, which lead to the critical temperature T c = 0.84(2) and a new universality class consistent with the set of critical exponents ν = 3/2, γ = 5/2, and β = 1/4. In order to gain further insight into the effects of the temperature gradient, we also develop a bond model that captures the magnetic film's growth dynamics. Our findings show that the interplay of geometry and thermal bath asymmetries leads to growth bond flux asymmetries and the onset of transverse ordering effects that explain qualitatively the shift observed in the critical temperature. The relevance of these mechanisms is further confirmed by a finite-size scaling analysis of the interface width, which shows that the growing sites of the system define a self-affine interface.

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Section: Introductionmentioning

confidence: 99%

Nonequilibrium critical behavior of magnetic thin films grown in a temperature gradient

Candia¹,

Albano²

2012

J. Stat. Mech.

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“…This is similar to the molecular dynamics approach, which solves deterministic evolution of a system described by Hamiltonian, i.e., it does not use random numbers. Previously, this algorithm has been used, among others, to simulate the electrocaloric effect in alloys [34], to study dynamics of discrete systems with long range interactions [35], or thermal conductivity in lattice systems without [36][37][38][39][40] and with an interface [41,42], where the lattice is typically attached to two heat baths at different temperatures. Our lattice system is in a homogeneous heat bath.…”

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confidence: 99%

Energy storage in steady states under cyclic local energy input

2020

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We study periodic steady states of a lattice system under external cyclic energy supply using simulation. We consider different protocols for cyclic energy supply and examine the energy storage. Under the same energy flux, we found that the stored energy depends on the details of the supply, period and amplitude of the supply. Further, we introduce an adiabatic wall as internal constrain into the lattice and examine the stored energy with respect to different positions of the internal constrain. We found that the stored energy for constrained systems are larger than their unconstrained counterpart. We also observe that the system stores more energy through large and rare energy delivery, comparing to small and frequent delivery. * Equilibrium states of the many body systems are well established. They are described by thermodynamics with its foundation justified by statistical mechanics. The central result of statistical mechanics, i.e., the equilibrium probability distribution of a system in a heat bath as given by the Boltzmann distribution, is considered to be the textbooks knowledge.Such a general framework for non-equilibrium steady states does not exist yet.Nonetheless, different approaches that address specific non-equilibrium situations have been developed. For non-equilibrium systems that fall under linear response regime, i.e., equilibrium systems under small perturbations, phenomenological arguments led to the formulation of the fluctuation-dissipation theorem (FDT) [1][2][3]. These systems can also be described by linear irreversible thermodynamics, which provides an expression for the entropy production in the form of affinities and fluxes [4,5]. Further developments concern the extension of FDT to non-equilibrium steady states (NESS). Various forms of FDTs were proposed, which link the response to a small perturbation from the NESS to the correlation functions in the NESS [3,6,7]. For systems in which fluctuations are eminent, results now known as the fluctuation theorems (FT) were proved, which are valid also for deep NESSs.These theorems establish restrictions on the probability distribution of quantities defined on trajectories [8,9]. Different FTs have been proved for a variety of systems such as chaotic [10] or stochastic systems [11], and for various processes such as diffusion [12] or relaxation [13]. The FTs for the probability distribution of work, were proved by Jarzynski and Crook [14,15]. By generalizing the concept of thermodynamic quantities on the trajectory level, these relations can be unified under the framework of stochastic thermodynamics [8]. They are particularly relevant for small systems such as molecular motors or nano-devicies [16,17], chemical reaction systems [18] and systems with strong fluctuations [19]. The central results of contemporary non-equilibrium thermodynamics are critically reviewed in Ref. [20].Here, we address the problem of energy storage in NESSs. It is interesting and relevant for potential applications, e.g., in energy harvesting [21], to know how the av...

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Dynamical and stationary critical behavior of the Ising ferromagnet in a thermal gradient

Cited by 2 publications

References 20 publications

Nonequilibrium critical behavior of magnetic thin films grown in a temperature gradient

Nonequilibrium critical behavior of magnetic thin films grown in a temperature gradient

Energy storage in steady states under cyclic local energy input

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