The Ising model below T<sub>c</sub>: calculation of nonuniversal amplitudes using a primitive droplet model

Harris, C K

doi:10.1088/0305-4470/17/3/009

Cited by 18 publications

(38 citation statements)

References 19 publications

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“…and H → −0. These expressions should be compared with the droplet theory predictions (1), (2). First, let us verify, that expressions (2) and (25) for the amplitude A are equivalent.…”

mentioning

confidence: 88%

“…It is widely accepted (for review, see [1]) that for all T < T c , the free energy F (H) of the two-dimensional Ising model analytically continued from the positive real axis H > 0 into the complex H-plane, has a branch cut singularity at the origin. Near the cut drawn along the negative real axis H < 0, the imaginary part of the free energy is believed to have the following form [2] Im F (e ±iπ | H |) = ∓B | H | exp (−A/ |H|) (1) for small |H|. This expression extrapolates to the Ising model the results obtained by Langer [3] and N.J. Günther et al [4] in the droplet field theory analysis of the coarse-grained Ginzburg-Landau model.…”

mentioning

confidence: 99%

“…To determine the decay rate Γ of the metastable vacuum we use the following nonregorous formal procedure. In the second order correction E (2) ms to the metastable vacuum energy we shift the excitation energy levels downwards into the complex E-plane:…”

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confidence: 99%

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Decay of the metastable phase ind=1andd=2Ising models

Rutkevich

1999

Phys. Rev. B

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We calculate perturbatively the tunneling decay rate Γ of the metastable phase in the quantum d = 1 Ising model in a skew magnetic field near the coexistence line 0 < hx < 1, hz → −0 at T = 0. It is shown that Γ oscillates in the magnetic field hz due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d = 2 Ising model at T < Tc, we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We find also evidence for the discrete-lattice corrections in this metastable phase free energy.

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“…and H → −0. These expressions should be compared with the droplet theory predictions (1), (2). First, let us verify, that expressions (2) and (25) for the amplitude A are equivalent.…”

mentioning

confidence: 88%

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confidence: 99%

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Decay of the metastable phase ind=1andd=2Ising models

Rutkevich

1999

Phys. Rev. B

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“…In the first equality, we have used μ ≈ 2H , which for the Ising model is a good approximation for T below the Curie temperature [32,33,43]. To conduct this test, we carry out new runs for the case of l = 7 over a range of βH from 0.048 to 0.056.…”

Section: Nucleation Theoremmentioning

confidence: 99%

Heterogeneous nucleation in the low-barrier regime

et al. 2013

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In simulations of the two-dimensional Ising model, we examine heterogeneous nucleation induced by a small impurity consisting of a line of l fixed spins. As l increases, we identify a limit of stability beyond which the metastable phase is not defined. We evaluate the free energy barrier for nucleation of the stable phase and show that, contrary to expectation, the barrier does not vanish on approach to the limit of stability. We also demonstrate that our values for the height of the barrier yield predictions for the nucleation time (from transition state theory) and the size of the critical cluster (from the nucleation theorem) that are in excellent agreement with direct measurements, even near the limit of stability.

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“…(24). This is obtained from calculations that do not involve the dynamics, such as analyses of series expansions [160,169,170] and transfer-matrix calculations [138,139,144]. These studies, as well as MC work [108,[171][172][173], also indicate that the free-energy cost of the critical droplet is given by Eq.…”

Section: Nucleationmentioning

confidence: 99%

Recent Results on the Decay of Metastable Phases

Rikvold

Gorman

1995

Annual Reviews of Computational Physics I

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 Ising model below T_c: calculation of nonuniversal amplitudes using a primitive droplet model

Cited by 18 publications

References 19 publications

Decay of the metastable phase ind=1andd=2Ising models

Decay of the metastable phase ind=1andd=2Ising models

Heterogeneous nucleation in the low-barrier regime

Recent Results on the Decay of Metastable Phases

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The Ising model below Tc: calculation of nonuniversal amplitudes using a primitive droplet model

Cited by 18 publications

References 19 publications

Decay of the metastable phase ind=1andd=2Ising models

Decay of the metastable phase ind=1andd=2Ising models

Heterogeneous nucleation in the low-barrier regime

Recent Results on the Decay of Metastable Phases

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Product

Resources

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The Ising model below T_c: calculation of nonuniversal amplitudes using a primitive droplet model