Recent Results on the Decay of Metastable Phases

Rikvold, Per Arne; Gorman, B. M.

doi:10.1142/9789812831682_0005

Cited by 67 publications

(150 citation statements)

References 155 publications

(457 reference statements)

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“…Naively, faster relaxation for larger systems may appear unexpected, but is easily explained using the wellknown nucleation theory of Kolmogorov-Johnson-MehlAvrami [22,23]. We assume that critical droplets of the stable phase are created with a small uniform rate ǫ per unit time per unit area, and once formed, the droplet radius grows at a constant rate v. Then, the probability that any randomly chosen site is still not invaded by the stable phase is given by exp[−ǫ t 0 dt ′ V (t ′ )], where V (t ′ ) is the area of the region such that a nucleation event within this area will reach the origin before time t ′ .…”

Section: Metastability Of the Nematic Phase For Large Activitiesmentioning

confidence: 99%

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

et al. 2013

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We study the phase transition from a nematic phase to a high-density disordered phase in systems of long rigid rods of length k on the square and triangular lattices. We use an efficient Monte Carlo scheme that partly overcomes the problem of very large relaxation times of nearly jammed configurations. The existence of a continuous transition is observed on both lattices for k = 7. We study correlations in the high-density disordered phase, and we find evidence of a crossover length scale ξ * 1400, on the square lattice. For distances smaller than ξ * , correlations appear to decay algebraically. Our best estimates of the critical exponents differ from those of the Ising model, but we cannot rule out a crossover to Ising universality class at length scales ≫ ξ * . On the triangular lattice, the critical exponents are consistent with those of the two dimensional three-state Potts universality class.

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Section: Metastability Of the Nematic Phase For Large Activitiesmentioning

confidence: 99%

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

et al. 2013

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“…(For reviews with an extensive list of references, see refs. [175,176].) Our present understanding of the phenomenon of nucleation is based largely on the work of Langer [177].…”

Section: Introductionmentioning

confidence: 99%

Non-perturbative renormalization flow in quantum field theory and statistical physics

2002

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We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative solutions follow from approximations to the general form of the coarse-grained free energy or effective average action. They interpolate between the microphysical laws and the complex macroscopic phenomena. Our approach yields a simple unified description for O(N )-symmetric scalar models in two, three or four dimensions, covering in particular the critical phenomena for the second-order phase transitions, including the Kosterlitz-Thouless transition and the critical behavior of polymer chains. We compute the aspects of the critical equation of state which are universal for a large variety of physical systems and establish a direct connection between microphysical and critical quantities for a liquid-gas transition. Universal features of first-order phase transitions are studied in the context of scalar matrix models. We show that the quantitative treatment of coarse graining is essential for a detailed estimate of the nucleation rate. We discuss quantum statistics in thermal equilibrium or thermal quantum field theory with fermions and bosons and we describe the high temperature symmetry restoration in quantum field theories with spontaneous symmetry breaking. In particular we explore chiral symmetry breaking and the high temperature or high density chiral phase transition in quantum chromodynamics using models with effective four-fermion interactions.This work is dedicated to the 60th birthday of Franz Wegner. *

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“…In order to address the question of hadronization after a first-order transition in a heavy ion collision picture, one should then perform finite-size real-time lattice simulations. In fact, lattice methods have been successfully applied to the study of homogeneous nucleation in different contexts [2,27,28]. One can thereby avoid the drawbacks implied by analytical approximations, such as the thin-wall hypothesis.…”

Section: ∼ O(10mentioning

confidence: 99%

“…On the other hand, systematic studies of finite size effects in the case of metastable decays and other nonequilibrium processes are rare [1,2]. In this paper, we discuss finite size effects on the dynamics of homogeneous nucleation in a first-order temperature-driven transition (For more details, see [3]).…”

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confidence: 99%

Finite-size constraints on nucleation of hadrons in a quark-gluon plasma

Fraga

Venugopalan

2004

Braz. J. Phys.

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We discuss finite-size effects on homogeneous nucleation in first-order phase transitions. We study their implications for cosmological phase transitions and to the hadronization of a quark-gluon plasma generated in high-energy heavy ion collisions.Finite-size scaling has achieved an immense success in the study of equilibrium critical phenomena. On the other hand, systematic studies of finite size effects in the case of metastable decays and other nonequilibrium processes are rare [1,2]. In this paper, we discuss finite size effects on the dynamics of homogeneous nucleation in a first-order temperature-driven transition (For more details, see [3]). In particular, we consider the case of cosmological phase transitions in the early universe [4], and that of a quark-gluon plasma (QGP) decay into hadronic matter in a high-energy heavy ion collision [5,6]. The former might provide sensible mechanisms to explain the baryon number asymmetry in the universe and primordial nucleosynthesis [7,8], whereas the latter is expected to be observed [9] at BNL Relativistic Heavy Ion Collider (RHIC). The length and time scales involved in each of these cases differ by several orders of magnitude.In the usual description of homogeneous nucleation [1], there are two ways in which the finite size of the system can affect the formation and evolution of bubbles and, consequently, the dynamics of phase conversion. Firstly, one has to consider the effects on the nucleation rate and the early stage growth of the bubbles. As will be shown below, this correction comes about through an intrinsic uncertainty in the determination of the supercooling undergone by the system. For the cases considered here, it brings only minor modifications to a description which assumes an infinite system. The second and, in general, most important finite-size effect is its influence on the domain coarsening process, or late-stage growth of the bubbles. The relevant length scales here are the typical size of the system, the radius of the critical bubble and the correlation length.In a continuum description of a first-order phase transition, it is common to consider a coarse-grained free energy, F , of the Landau-Ginzburg form with temperaturedependent coefficients [1]. (In the case of QCD, such a free energy can be obtained, for instance, from the oneloop effective potential of a linear sigma model coupled to quarks [10,11].) The nucleation rate can be expressed as Γ = P e −F b /T , where F b is the free energy of a critical bubble, with radius R c , and the prefactor P measures statistical and dynamical fluctuations about the saddle point of the Euclidean action in functional space. It is convenient to write the prefactor P as a product of the bubble's growth rate and a factor proportional to the ratio of the determinant of the fluctuation operator around the bubble configuration relative to that around the homogeneous metastable state [12]. For the relativistic case, in the thin-wall limit, we have [13]:Here, η and ξ are respectively the shear viscosity and ...

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Recent Results on the Decay of Metastable Phases

Cited by 67 publications

References 155 publications

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices

Non-perturbative renormalization flow in quantum field theory and statistical physics

Finite-size constraints on nucleation of hadrons in a quark-gluon plasma

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