Goldstone modes in vacuum decay and first-order phase transitions

Günther, Neil J.; Wallace, D. J.; Nicole, Denis A.

doi:10.1088/0305-4470/13/5/034

Cited by 130 publications

(155 citation statements)

References 39 publications

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“…There are many possible further applications of this technique, as there are many semiclassical problems where the classical solution, about which one is computing the quantum fluctuations, has radial symmetry. Closely related possible applications include: (i) metastable decay in theories with more than one field [36], where analytic and approximate approaches to the prefactor are quite difficult, but a direct numerical approach might be more useful; (ii) models in dimensions other than 4, which have been studied in and beyond the thin-wall approximation [6,13,14,37]; (iii) an extension to finite temperature, where the high temperature limit is essentially a dimensionally reduced 3d radial problem [9,10], but for intermediate temperatures the explicit summation over Matsubara modes is necessary. This technique for computing precisely the fluctuation contribution may also be useful for a set of fascinating questions concerning the validity of Langer's homogeneous nucleation picture itself, as well as the semiclassical approximation [38].…”

Section: Discussionmentioning

confidence: 99%

Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay

Dunne

2005

Phys. Rev. D

127

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We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a selfinteracting scalar field theory modeling the process of nucleation in four dimensional spacetime.This technique does not rely on the thin-wall approximation. The method is based on the GelfandYaglom approach to determinants of differential operators, suitably extended to higher dimensions using angular momentum cutoff regularization. A related approach has been discussed recently by Baacke and Lavrelashvili, but we implement the regularization and renormalization in a different manner, and compare directly with analytic computations made in the thin-wall approximation.We also derive a simple new formula for the zero mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behavior of the classical bounce solution. * Electronic address: dunne@phys.uconn.edu † Electronic address: hsmin@dirac.uos.ac.kr

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Section: Discussionmentioning

confidence: 99%

Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay

Dunne

2005

Phys. Rev. D

127

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“…The values of the parameters H0, L, and T have been selected such that switching occurs via the multi-droplet mechanism. The constants Ξ0(T ) and K are calculated from droplet theory [74][75][76][77] for two-dimensional Ising systems. The constants τ and r are measured from field-reversal MC simulations with the Glauber dynamic (using the parameters listed in the left column).…”

Section: Discussionmentioning

confidence: 99%

Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition

1999

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Hysteresis is studied for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in a sinusoidally oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on large systems and moderately strong field amplitudes at a temperature below Tc. In this parameter regime, the magnetization switches through random nucleation and subsequent growth of many droplets of spins aligned with the applied field. Using a time-dependent extension of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of metastable decay, we analyze the statistical properties of the hysteresis-loop area and the correlation between the magnetization and the field. This analysis enables us to accurately predict the results of extensive Monte Carlo simulations. The average loop area exhibits an extremely slow approach to an asymptotic, logarithmic dependence on the product of the amplitude and the field frequency. This may explain the inconsistent exponent estimates reported in previous attempts to fit experimental and numerical data for the low-frequency behavior of this quantity to a power law. At higher frequencies we observe a dynamic phase transition. Applying standard finite-size scaling techniques from the theory of second-order equilibrium phase transitions to this nonequilibrium transition, we obtain estimates for the transition frequency and the critical exponents (β/ν ≈ 0.11, γ/ν ≈ 1.84 and ν ≈ 1.1). In addition to their significance for the interpretation of recent experiments on switching in ferromagnetic and ferroelectric nanoparticles and thin films, our results provide evidence for the relevance of universality and finite-size scaling to dynamic phase transitions in spatially extended nonstationary systems. PACS number(s): 05.40.+j, 77.80.Dj, 64.60.Qb

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“…The integral in (27) can then be identified as the one loop correction to the classical potential, while the remaining terms represent the quantum corrections due to fluctuations around the bounce wall [16]. Then, by using Eqs.…”

Section: The Vacuum Decay Rate and The Bounce Solutionmentioning

confidence: 99%

TUNNELING AND NUCLEATION RATE IN THE $(\frac{\lambda}{4!} \phi^4 +\frac{\sigma}{6!} \phi^6)_3$ MODEL

Flores

Svaiter

Ramos

1999

Int. J. Mod. Phys. A

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Goldstone modes in vacuum decay and first-order phase transitions

Cited by 130 publications

References 39 publications

Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay

Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay

Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition

TUNNELING AND NUCLEATION RATE IN THE $(\frac{\lambda}{4!} \phi^4 +\frac{\sigma}{6!} \phi^6)_3$ MODEL

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