Critical droplets and metastability for a Glauber dynamics at very low temperatures

Neves, E. Jordão; Schonmann, Roberto H.

doi:10.1007/bf02431878

Cited by 151 publications

(163 citation statements)

References 8 publications

Supporting

Mentioning

153

Contrasting

Order By: Relevance

“…The proof of this lemma is the standard one, see, for instance, [NS1,KO1,KO2] or the proof of Proposition 4.1 in [CO]. One has to consider the basin of attraction of the local minimum R l,m and work out the minimum of the energy on its boundary.…”

Section: Remarksmentioning

confidence: 99%

“…The metastable behavior of the nearest neighbor two dimensional Ising model for large finite volumes and small magnetic fields was analyzed in [NS1,NS2] in the zero temperature limit in the framework of the "pathwise approach" introduced in [CGOV]. In…”

Section: Introductionmentioning

confidence: 99%

“…In the same asymptotic regime as in [NS1], different Ising-like hamiltonians have been considered in [KO1,KO2,NO] and the three dimensional nearest neighbor Ising model has been studied in [BC]. In [CO] the Blume-Capel model has been studied (see also [FGRN] for a study of a version of this model with weak long range interactions) and in [OS1,OS2] the problem of metastability has been investigated in a more general case.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Untitled

Cirillo

Lebowitz

1998

Journal of Statistical Physics

View full text Add to dashboard Cite

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T → 0, h → 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.

show abstract

Section: Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Untitled

Cirillo

Lebowitz

1998

Journal of Statistical Physics

View full text Add to dashboard Cite

show abstract

“…Parts (a)-(b), together with the crude estimate lim β→∞ (1/β) log E (τ ) = Γ , were proved in [22]. Parts (c)-(e) were proved in [10].…”

Section: Glauber Dynamicsmentioning

confidence: 91%

“…(Neves and Schonmann [22], Bovier and Manzo [10]) (a) There exists a set of configurations C * S such that…”

Section: Glauber Dynamicsmentioning

confidence: 99%

Three Lectures on Metastability Under Stochastic Dynamics

Hollander

2009

Lecture Notes in Mathematics

View full text Add to dashboard Cite

Kinetics of fractal Ising clusters ‐ a Monte Carlo study

Stauffer

1992

Annalen der Physik

View full text Add to dashboard Cite

Abstract. For short times and small clusters we check the validity of the 1935 Becker-Doring equation by Monte Carlo simulations in the square Ising model at and near its critical point; some discrepancies are found.Keywords: Clusters; Ising model; Relaxation.Droplet models for collective phenomena in fluids are quite old and have served a useful role in the prediction of phase transition properties. In some sense these droplets are the elementary excitations of fluids, just as phonons are elementary excitations in solids, and photons build up the radiation field. In the Debye theory for the specific heat of solids, we do not sum over all individual atoms, as Einstein did; instead we sum up the energy contribution from all phonons. Similarly, droplet models for fluids try to describe the fluid properties as a superposition of contributions from single droplets. Both the question of droplet-droplet interactions and the applicability of macroscopic droplet concepts to clusters containing one to ten atoms only have been controversial for many years, as has been even the definition itself of a droplet.More than half century ago, this journal published the Becker-Doring formula for droplet growth and decay [l]. Collective phenomena at liquid-gas (and analogous other) transitions have been described since 70 years by cluster or droplet models Here n, ( t ) is the actual time-dependent number of suitably defined clusters (droplets) containing s liquid molecules each, and N , is the equilibrium limit of that number; R , is the rate at which an s-cluster grows to size s + 1, and B, is the backward rate from size s + 1 to sizes. The current of net cluster growth from s to s + 1 isj, = R , n, -B , n,, , and must be zero in equilibrium: R, N , = B, N,,,. Thus the non-equilibrium current can be written asj, = R , N, (n,/N, -ns+l/Ns+r). The rate at which the actual cluster

show abstract

Critical droplets and metastability for a Glauber dynamics at very low temperatures

Cited by 151 publications

References 8 publications

Untitled

Untitled

Three Lectures on Metastability Under Stochastic Dynamics

Kinetics of fractal Ising clusters ‐ a Monte Carlo study

Contact Info

Product

Resources

About