Metastable reverse-phase droplets are calculated by renormalization-group theory by evaluating the magnetization of a droplet under magnetic field, matching the boundary condition with the reverse phase and noting whether the reverse-phase magnetization sustains. The maximal metastable droplet size and the discontinuity across the droplet boundary are thus calculated as a function of field and temperature for the Ising model in three dimensions. The method also yields hysteresis loops for finite systems, as function of temperature and system size.
The existence and limits of metastable droplets have been calculated using finite-system renormalization-group theory, for q-state Potts models in spatial dimension d=3. The dependence of the droplet critical sizes on magnetic field, temperature, and number of Potts states q has been calculated. The same method has also been used for the calculation of hysteresis loops across first-order phase transitions in these systems. The hysteresis loop sizes and shapes have been deduced as a function of magnetic field, temperature, and number of Potts states q. The uneven appearance of asymmetry in the …
We consider the problem of metastability in a probabilistic cellular automaton (PCA) with a parallel updating rule which is reversible with respect to a Gibbs measure. The dynamical rules contain two parameters $β$ and $h$ which resemble, but are not identical to, the inverse temperature and external magnetic field in a ferromagnetic Ising model; in particular, the phase diagram of the system has two stable phases when $β$ is large enough and $h$ is zero, and a unique phase when $h$ is nonzero. When the system evolves, at small positive values of $h$, from an initial state with all spins down,…
The contradiction between the stationary aproach to the density profile and the avalanche character of the metastable phase consumption is investigated. The exact solution for the metastable phase profile is obtained. The reconsidered value for the special parameter responsible for the hierarchy in the structure of the density profile around the droplet is presented.
The theory for manifestation of stochastic appearance of embryos in the global decay of metastable phase has been constructed. The regime of droplets growth is supposed to be both free molecular one and diffusion one. The deviation for a mean droplets number from the value predicted by the theory based on averaged characteristics have been calculated. The value of dispersion for the distribution of the total droplets number in particular attempt has been also calculated analytically. Comparison with results of numerical simulation has been given and the correspondence between simulation and an…
Stochastic features of decay of a metastable phase have been investigated with the help of a new monodisperse approximation. This approximation is more precise than the already used one and namely it allows to give a very simple but rather precise way to calculate dispersion of the total droplets number initiated by stochastic appearance of supercritical embryos. The derivation is done for a free molecular regime of droplets growth but the diffusion regime is also discussed.
Nucleation is considered near the pseudospinodal in a one-dimensional $ϕ^4$ model with a non-conserved order parameter and long-range interactions. For a sufficiently large system or a system with slow relaxation to metastable equilibrium, there is a non-negligible probability of nucleation occurring before reaching metastable equilibrium. This process is referred to as transient nucleation. The critical droplet is defined to be the configuration of maximum likelihood that is dynamically balanced between the metastable and stable wells. Time-dependent droplet profiles and nucleation rates are …
We study homogeneous nucleation from a deeply quenched metastable liquid to a spatially modulated phase. We find, for a general class of density functional theories, that the universally favored nucleating droplet in dimensions $d \geq 3$ is spherically symmetric with radial modulations resembling the layers of an onion. The existence of this droplet has important implications for systems with effective long-range interactions, and potentially applies to polymers, plasmas, and metals.
The equilibrium density distribution and thermodynamic properties of a Lennard-Jones fluid confined to nano-sized spherical cavities at constant chemical potential was determined using Monte Carlo simulations. The results describe both a single cavity with semipermeable walls as well as a collection of closed cavities formed at constant chemical potential. The results are compared to calculations using classical Density Functional Theory (DFT). It is found that the DFT calculations give a quantitatively accurate description of the pressure and structure of the fluid. Both theory and simulation…
We study by kinetic Monte Carlo simulations the dynamic behavior of a Ziff-Gulari-Barshad model with CO desorption for the reaction CO + O $\to$ CO$_2$ on a catalytic surface. Finite-size scaling analysis of the fluctuations and the fourth-order order-parameter cumulant show that below a critical CO desorption rate, the model exhibits a nonequilibrium first-order phase transition between low and high CO coverage phases. We calculate several points on the coexistence curve. We also measure the metastable lifetimes associated with the transition from the low CO coverage phase to the high CO cove…
The barriers between metastable states near the glass transition of a random heteropolymer are studied using replicas by describing inhomogeneous states. The instanton solution for a replica space free energy functional is found numerically to estimate the size of activation barriers and of the critical nuclei themselves between the dynamic and the static glass transition temperatures.
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 $0<h_{x}<1, h_{z}\to -0$ at T=0. It is shown that $Γ$ oscillates in the magnetic field $h_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d=2 Ising model at $T<T_c$, 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 t…
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 $T\to 0$, $h\to 0$ 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 f…
We consider the effect of droplet excitations in the random first order transition theory of glasses on the configurational entropy. The contribution of these excitations is estimated both at and above the ideal glass transition temperature. The temperature range where such excitations could conceivably modify or `round-out' an underlying glass transition temperature is estimated, and found to depend strongly on the surface tension between locally metastable phases in the supercooled liquid. For real structural glasses this temperature range is found to be very narrow, consistent with the quan…
Using molecular simulation, we study the nucleation of liquid droplets from binary mixtures and determine the free energy of nucleation along entropic pathways. To this aim, we develop the $μ_1 μ_2 VT-S$ method, based on the grand-canonical ensemble modeling the binary mixture, and use the entropy of the system $S$ as the reaction coordinate to drive the formation of the liquid droplet. This approach builds on the advantages of the grand-canonical ensemble, which allows for the direct calculation of the entropy of the system and lets the composition of the system free to vary throughout the nu…
The role of metastable liquid phases in vapor-crystal nucleation is studied using Density Functional Theory(DFT). The model gives a semi-quantitatively accurate description of both the vapor-liquid-solid phase diagram for both simple fluids (Lennard-Jones interactions) and of the low-density/high-density/crystal phase diagram for model globular proteins (ten Wolde-Frenkel interaction). The density profile is characterized by two local order parameters, the average density and the crystallinity. The bulk free energy model is supplemented by squared-derivative terms in these order parameters to …
How Continuous Symmetry Stabilizes the Ordered Phase of Polar Flocks
University of Chicago（芝加哥大学）；CEA, CNRS Université Paris-Saclay（巴黎萨克雷大学CEA/CNRS）；Computational Science Research Center, Beijing（北京计算科学研究中心）；Sorbonne Université, CNRS（索邦大学/CNRS）；Technion – Israel Institute of Technology（以色列理工学院）；Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）
We study the solid-to-liquid transition in a two-dimensional fully periodic soft-glassy model with an imposed spatially heterogeneous stress. The model we consider consists of droplets of a dispersed phase jammed together in a continuous phase. When the peak value of the stress gets close to the yield stress of the material, we find that the whole system intermittently tunnels to a metastable "fluidized" state, which relaxes back to a metastable "solid" state by means of an elastic-wave dissipation. This macroscopic scenario is studied through the microscopic displacement field of the droplets…
We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multi-droplet regime where the metastable phase decays through nucleation and growth of many droplets of the stable phase. At a critical frequency, the system undergoes a genuine non-equilibrium phase transition, in which the symmetry-broken phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. We investigate the universal aspects of this dynamic phase transition at various temperatures and fi…
We focus on the Gibbs free energy $ΔG$ for nucleating a droplet of the stable phase (e.g. solid) inside the metastable parent phase (e.g. liquid), close to the first-order transition temperature. This quantity is central to the theory of homogeneous nucleation, since it superintends the nucleation rate. We recently introduced a field theory describing the dependence of $ΔG$ on the droplet volume $V$, taking into account besides the microscopic fuzziness of the droplet-parent interface, also small fluctuations around the spherical shape whose effect, assuming isotropy, was found to be a charact…
The Monte Carlo with Absorbing Markov Chains (MCAMC) method is introduced. This method is a generalization of the rejection-free method known as the $n$-fold way. The MCAMC algorithm is applied to the study of the very low-temperature properties of the lifetime of the metastable state of Ising ferromagnets. This is done both for square-lattice and cubic-lattice nearest-neighbor models. Comparison is made with exact low-temperature predictions, in particular the low-temperature predictions that the metastable lifetime is discontinuous at particular values of the field. This discontinuity for th…
We study thermally activated dynamics using functional renormalization within the field theory of randomly pinned elastic systems, a prototype for glasses. It appears through an essentially non-perturbative boundary layer in the running effective action, for which we find a consistent scaling ansatz to all orders. We find that in the statics the boundary layer describes the physics of rare low energy metastable states as suggested by a phenomenological droplet picture. The extension to equilibrium dynamics mandates a non-trivial broad distribution of relaxation times for the large scale modes,…
The general formalism of homogeneous nucleation theory is applied to study the hadronization pattern of the ultra-relativistic quark-gluon plasma (QGP) undergoing a first order phase transition. A coalescence model is proposed to describe the evolution dynamics of hadronic clusters produced in the nucleation process. The size distribution of the nucleated clusters is important for the description of the plasma conversion. The model is most sensitive to the initial conditions of the QGP thermalization, time evolution of the energy density, and the interfacial energy of the plasma-hadronic matte…
The problem of metastability for a stochastic dynamics with a parallel updating rule is addressed in the Freidlin--Wentzel regime, namely, finite volume, small magnetic field, and small temperature. The model is characterized by the existence of many fixed points and cyclic pairs of the zero temperature dynamics, in which the system can be trapped in its way to the stable phase. %The characterization of the metastable behavior %of a system in the context of parallel dynamics is a very difficult task, %since all the jumps in the configuration space are allowed. Our strategy is based on recent p…
