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Blume, M.

doi:10.1103/physrev.141.517

Cited by 1,027 publications

(538 citation statements)

References 16 publications

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“…the saving behavior, in the present model) with those observed in the reference group, will increase with the perceived difference in those actions and beliefs. In physics, a Hamiltonian of the above type have been used, for instance, in the Blume-Capel model [15,16]. A similar herding behavior is observed for the agents' expectations: the expectations of the individuals, with respect to the future market behavior, will tend to conform with the opinion of their social surrounding.…”

Section: The Modelmentioning

confidence: 89%

Statistical Economics on Multi-Variable Layered Networks

Erez¹,

Hohnisch²,

Solomon³

2005

Economics: Complex Windows

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Abstract. We propose a Statistical-Mechanics inspired framework for modeling economic systems. Each agent composing the economic system is characterized by a few variables of distinct nature (e.g. saving ratio, expectations, etc.). The agents interact locally by their individual variables: for example, people working in the same office may influence their peers' expectations (optimism/pessimism are contagious) , while people living in the same neighborhood may influence their peers' saving patterns (stinginess/largeness are contagious). Thus, for each type of variable there exists a different underlying social network, which we refer to as a "layer". Each layer connects the same set of agents by a different set of links defining a different topology. In different layers, the nature of the variables and their dynamics may be different (Ising, Heisenberg, matrix models, etc). The different variables belonging to the same agent interact (the level of optimism of an agent may influence its saving level), thus coupling the various layers. We present a simple instance of such a network, where a one-dimensional Ising chain (representing the interaction between the optimist-pessimist expectations) is coupled through a random site-to-site mapping to a one-dimensional generalized BlumeCapel chain (representing the dynamics of the agents' saving ratios). In the absence of coupling between the layers, the one-dimensional systems describing respectively the expectations and the saving ratios do not feature any ordered phase (herding). Yet, such a herding phase emerges in the coupled system, highlighting the non-trivial nature of the present framework.⋆ Corresponding Author. Email: etom@pob.huji.ac.il.Tom thanks "SARA Computing and Networking Services" for generously providing machine time for the simulations. ⋆⋆ M.H. gratefully acknowledges financial support from DFG grant TR120/12-1.

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Section: The Modelmentioning

confidence: 89%

Statistical Economics on Multi-Variable Layered Networks

Erez¹,

Hohnisch²,

Solomon³

2005

Economics: Complex Windows

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“…The BC model was originally introduced independently by Blume [1] and Capel [2] in quite different contexts. The Hamiltonian for the BC model is given by ( )…”

Section: Model and Methodologymentioning

confidence: 99%

“…The Blume-Capel (BC) model is a spin-1 Ising model with bilinear (J) and a single-ion potential or crystal-field interaction (D) that was originally proposed, by Blume [1] and Capel [2] independently, to study magnetic systems. The BC model is one of the well known prototype models used to examine various physical systems, such as multicomponent fluids, ternary alloys, microemulsions, ordering in semiconductor alloys, electronic conduction models, metallic alloys, polymeric systems, proteins and liquid crystals (see [3] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Dynamic phase diagrams of the Blume–Capel model in an oscillating field by the path probability method

Ertaş¹,

Keskín²

2014

Physica A: Statistical Mechanics and its Applications

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We calculate the dynamic phase transition (DPT) temperatures and present the dynamic phase diagrams in the Blume-Capel model under the presence of a time-dependent oscillating external magnetic field by using the path probability method. We study the time variation of the average order parameters to obtain the phases in the system and the paramagnetic (P), ferromagnetic (F) and the F + P mixed phases are found. We also investigate the thermal behavior of the dynamic order parameters to analyze the nature (continuous and discontinuous) of transitions and to obtain the DPT points. We present the dynamic phase diagrams in three planes, namely (T, h), (d, T) and (k 2 /k 1 , T), where T is the reduced temperature, h the reduced magnetic field amplitude, d the reduced crystal-field interaction and the k 2 , k 1 rate constants. The phase diagrams exhibit dynamic tricritical and reentrant behaviors as well as a double critical end point and triple point, strongly depending on the values of the interaction parameters and the rate constants. We compare and discuss the dynamic phase diagrams with dynamic phase diagrams that are obtained within the Glauber-type stochastic dynamics based on the mean-field theory and the effective field theory.

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“…Notice that our convention on D differs from the literature. 23,24 H is an external magnetic field applied to the spin system. The spin Hamiltonian ͓Eq.…”

Section: Formalism For Phonon-assisted Transition Ratesmentioning

confidence: 99%

Transition rates for aS≥1spin model coupled to ad-dimensional phonon bath

Park

2008

Phys. Rev. B

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We consider a S Ն 1 spin model ͑or a generalized Blume-Capel model͒ weakly coupled to a d-dimensional phonon bath and investigate transition rates between different spin configurations. This study is motivated by understanding magnetization relaxation as a function of temperature in diverse magnetic systems such as arrays of magnetic nanoparticles and magnetic molecules. We assume that the magnetization of the spin system relaxes through consecutive emission or absorption of a single phonon. From a weak, linear spin-phonon coupling Hamiltonian, we derive transition rates that would be used to examine dynamic properties of the system in kinetic Monte Carlo simulations. Although the derived phonon-assisted transition rates satisfy detailed balance, in the case of two-and three-dimensional phonon baths, transitions between degenerate states are not allowed. ͑This is a major difference of the phonon-assisted transition rates from the Metropolis and Glauber transition rates.͒ Thus, if there are no alternative paths along which the spin system can relax, the relaxation time diverges. Otherwise, the system finds other paths, which leads to an increase in the relaxation time and energy barrier. However, when higher-order phonon processes are included in the transition rates, it is found that the system can reach the states which were inaccessible due to the forbidden transitions. As a result, the system recovers some of the dynamic properties obtained using the Glauber transition rate.

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Theory of the First-Order Magnetic Phase Change in UO2

Cited by 1,027 publications

References 16 publications

Statistical Economics on Multi-Variable Layered Networks

Statistical Economics on Multi-Variable Layered Networks

Dynamic phase diagrams of the Blume–Capel model in an oscillating field by the path probability method

Transition rates for aS≥1spin model coupled to ad-dimensional phonon bath

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