Phase diagrams of the spin-1 Ising Blume-Emery-Griffiths model: Monte Carlo simulations

Wang, Yung‐Li; Lee, Felix; Kimel, J.D.

doi:10.1103/physrevb.36.8945

Cited by 102 publications

(36 citation statements)

References 17 publications

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“…[40][41][42][43]). We note that these interesting and relevant studies concern models with short-range interactions, where it suffices to study the canonical ensemble, since ensemble equivalence occurs.…”

Section: Discussionmentioning

confidence: 99%

Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model

et al. 2017

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We study inequivalence of canonical and microcanonical ensembles in the mean-field BlumeEmery-Griffiths model. This generalizes previous results obtained for the Blume-Capel model. The phase diagram strongly depends on the value of the biquadratic exchange interaction K, the additional feature present in the Blume-Emery-Griffiths model. At small values of K, as for the Blume-Capel model, lines of first and second order phase transitions between a ferromagnetic and a paramagnetic phase are present, separated by a tricritical point whose location is different in the two ensembles. At higher values of K the phase diagram changes substantially, with the appearance of a triple point in the canonical ensemble which does not find any correspondence in the microcanonical ensemble. Moreover, one of the first order lines that starts from the triple point ends in a critical point, whose position in the phase diagram is different in the two ensembles. This line separates two paramagnetic phases characterized by a different value of the quadrupole moment. These features were not previously studied for other models and substantially enrich the landscape of ensemble inequivalence, identifying new aspects that had been discussed in a classification of phase transitions based on singularity theory. Finally, we discuss ergodicity breaking, which is highlighted by the presence of gaps in the accessible values of magnetization at low energies: it also displays new interesting patterns that are not present in the Blume-Capel model.

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Section: Discussionmentioning

confidence: 99%

Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model

et al. 2017

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“…Let us first briefly recall the nature of the phases of the latter. Several studies ( [13,19,20]) shows the presence of ferromagnetic, paramagnetic, predominant vacancies and anti-quadrupolar phases whose typical configurations are lattices with two sublattices, one with spins equal to zero, one with alternated spins −1, +1. These configurations do not appear for the range of parameters for which we have a correspondence with our variant of the Schelling model.…”

Section: Discussionmentioning

confidence: 99%

Schelling segregation in an open city: A kinetically constrained Blume-Emery-Griffiths spin-1 system

2010

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In the 70's Schelling introduced a multi-agent model to describe the segregation dynamics that may occur with individuals having only weak preferences for 'similar' neighbors. Recently variants of this model have been discussed, in particular, with emphasis on the links with statistical physics models. Whereas these models consider a fixed number of agents moving on a lattice, here we present a version allowing for exchanges with an external reservoir of agents. The density of agents is controlled by a parameter which can be viewed as measuring the attractiveness of the city-lattice. This model is directly related to the zero-temperature dynamics of the Blume-Emery-Griffiths (BEG) spin-1 model, with kinetic constraints. With a varying vacancy density, the dynamics with agents making deterministic decisions leads to a new variety of "phases" whose main features are the characteristics of the interfaces between clusters of agents of different types. The domains of existence of each type of interface are obtained analytically as well as numerically. These interfaces may completely isolate the agents leading to another type of segregation as compared to what is observed in the original Schelling model, and we discuss its possible socio-economic correlates.

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“…We also study the behavior of the dynamic magnetic hysteresis and investigate the effects of the frequency on hysteresis properties. The reason for studying the nonequilibrium aspects of the system with repulsive biquadratic coupling is that Ising systems for K/J < 0 display the reach and interesting equilibrium (see [19][20][21][22][23] and references therein) and nonequilibrium or dynamic [24,25] behavior.…”

Section: Introductionmentioning

confidence: 99%

Multicritical Dynamic Phase Diagrams and Dynamic Hysteresis Loops in a Mixed Spin-2 and Spin-5/2 Ising Ferrimagnetic System with Repulsive Biquadratic Coupling: Glauber Dynamic Approach

2012

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The stationary states of the kinetic mixed spin-2 and spin-5/2 Ising ferrimagnetic system with repulsive biquadratic coupling are examined within a mean-field approach under the presence of a time varying (sinusoidal) magnetic field. We employ Glauber-type stochastic dynamics to construct a set of coupled mean-field dynamic equations, and we solve these equations to find the phases in the system. We also investigate the thermal behavior of the dynamic order parameters to characterize the nature (continuous or discontinuous) of the dynamic phase transitions (DPTs) and obtain the DPT points. The phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane, and a comparison is made with the results of other kinetic mixed spin systems. We also study the behavior of the dynamic magnetic hysteresis and investigate the effects of the frequency on hysteresis properties, and we find the results are in good agreement with some previous theoretical and experimental works.

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Phase diagrams of the spin-1 Ising Blume-Emery-Griffiths model: Monte Carlo simulations

Cited by 102 publications

References 17 publications

Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model

Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model

Schelling segregation in an open city: A kinetically constrained Blume-Emery-Griffiths spin-1 system

Multicritical Dynamic Phase Diagrams and Dynamic Hysteresis Loops in a Mixed Spin-2 and Spin-5/2 Ising Ferrimagnetic System with Repulsive Biquadratic Coupling: Glauber Dynamic Approach

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