Finite-range-scaling analysis of metastability in an Ising model with long-range interactions

Gorman, B. M.; Rikvold, Per Arne; Novotny, M. A.

doi:10.1103/physreve.49.2711

Cited by 12 publications

(29 citation statements)

References 52 publications

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“…In systems with effective long-range interactions we expect the change from metastability to instability of the LS phase to take place at a sharply defined mean-field spinodal point. 4 This leads to a threshold behavior with respect to the irradiation intensity, 4,19,20 which is qualitatively different from the gradual crossover seen in short-range models. 21 Here, we therefore investigate the LS-to-HS transition time and its dependence on the system size as functions of the irradiation intensity.…”

Section: Introductionmentioning

confidence: 82%

Threshold phenomena under photoexcitation of spin-crossover materials with cooperativity due to elastic interactions

et al. 2009

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Photo-induced switching from the low-spin state to the high-spin state is studied in a model spin-crossover material with long-range interactions induced by elastic distortions due to different molecular sizes of the two spin states. At a threshold value of the light intensity, nonequilibrium critical behavior is observed in the form of a jump in the high-spin fraction, corresponding to a mean-field spinodal point. Finite-size scaling of the divergence of the transition time is revealed through kinetic Monte Carlo simulations.

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Section: Introductionmentioning

confidence: 82%

Threshold phenomena under photoexcitation of spin-crossover materials with cooperativity due to elastic interactions

et al. 2009

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“…For the Q1DI model R=N and d=1 [152,156]. By solving the Euler-Lagrange equation numerically, one can also take into account the corrections to the expansion, as well as discrete lattice effects [94]. The prefactor to the Van't Hoff-Arrhenius term in |Im f | can be calculated by expanding the free-energy density functional about the stationary points corresponding to the metastable phase and the critical droplet.…”

Section: Nucleationmentioning

confidence: 99%

“…where B(T ) is a nonuniversal function of T , V is the system volume, and V ′ is the volume of the subspace in which the droplet itself is free to move without a cost in free energy. For the Q1DI model, [94]. From Eqs.…”

Section: Nucleationmentioning

confidence: 99%

Recent Results on the Decay of Metastable Phases

Rikvold

Gorman

1995

Annual Reviews of Computational Physics I

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142

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We review some aspects of current knowledge regarding the decay of metastable phases in many-particle systems. In particular we emphasize recent theoretical and computational developments and numerical results regarding homogeneous nucleation and growth in kinetic Ising and lattice-gas models. An introductory discussion of the droplet theory of homogeneous nucleation is followed by a discussion of Monte Carlo and transfer-matrix methods commonly used for numerical study of metastable decay, including some new algorithms. Next we discuss specific classes of systems. These include a brief discussion of recent progress for fluids, and more exhaustive considerations of ferromagnetic Ising models (i.e., attractive lattice-gas models) with weak long-range interactions and with short-range interactions. Whereas weak-long-range-force (WLRF) models have infinitely long-lived metastable phases in the infinite-range limit, metastable phases in short-range-force (SRF) models eventually decay, albeit extremely slowly. Recent results on the finitesize scaling of metastable lifetimes in SRF models are reviewed, and it is pointed out that such effects may be experimentally observable.

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“…The application of such ideas to a fieldtheoretical droplet model with Fokker-Planck dynamics has shown that close to coexistence, the nucleation rate for droplets of the equilibrium phase is proportional to the imaginary part of a complex-valued constrained free energy obtained by analytic continuation from the equilibrium phase into the metastable phase [8][9][10]. long-range forces [13][14][15] by a constrained-transfer-matrix method introduced by one of us [16]. Although no dynamical aspects were explicitly considered to obtain the constrained free energies, the average free-energy cost of a critical droplet was obtained over a wide range of fields and temperatures, in good agreement with the predictions of field-theoretical droplet models [8][9][10]14,15,17] and Monte Carlo (MC) simulations [1,[4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…long-range forces [13][14][15] by a constrained-transfer-matrix method introduced by one of us [16]. Although no dynamical aspects were explicitly considered to obtain the constrained free energies, the average free-energy cost of a critical droplet was obtained over a wide range of fields and temperatures, in good agreement with the predictions of field-theoretical droplet models [8][9][10]14,15,17] and Monte Carlo (MC) simulations [1,[4][5][6]. These results indicate the relevance of purely static properties, such as the free energy, to the relaxation behavior of metastable phases.…”

Section: Introductionmentioning

confidence: 99%

Method to study relaxation of metastable phases: Macroscopic mean-field dynamics

1995

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We propose two different macroscopic dynamics to describe the decay of metastable phases in many-particle systems with local interactions. These dynamics depend on the macroscopic order parameter m through the restricted free energy F (m) and are designed to give the correct equilibrium distribution for m. The connection between macroscopic dynamics and the underlying microscopic dynamic are considered in the context of a projectionoperator formalism. Application to the square-lattice nearest-neighbor Ising ferromagnet gives good agreement with droplet theory and Monte Carlo simulations of the underlying microscopic dynamic. This includes quantitative agreement for the exponential dependence of the lifetime τ on the inverse of the applied field H, and the observation of distinct field regions in which Λ ≡ d ln τ /d|H| 1−d depends differently on |H|. In addition, at very low temperatures we observe oscillatory behavior of Λ with respect to |H|, due to the discreteness of the lattice and in agreement with rigorous results. Similarities and differences between this work and earlier works on finite Ising models in the fixed-magnetization ensemble are discussed.PACS Numbers: 64.60 My, 64.60 Qb, 02.70.Lq, 05.50 +q Typeset using REVT E XRecently, complex-valued constrained free energies were numerically obtained for both the two-dimensional nearest-neighbor Ising ferromagnet [11,12] and for models with weak

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Finite-range-scaling analysis of metastability in an Ising model with long-range interactions

Cited by 12 publications

References 52 publications

Threshold phenomena under photoexcitation of spin-crossover materials with cooperativity due to elastic interactions

Threshold phenomena under photoexcitation of spin-crossover materials with cooperativity due to elastic interactions

Recent Results on the Decay of Metastable Phases

Method to study relaxation of metastable phases: Macroscopic mean-field dynamics

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