scholarly journals Symmetry-adapted order parameters and free energies for solids undergoing order-disorder phase transitions

2017 ◽  
Vol 96 (13) ◽  
Author(s):  
Anirudh Raju Natarajan ◽  
John C. Thomas ◽  
Brian Puchala ◽  
Anton Van der Ven
Keyword(s):  
Phase Transitions ◽  
Order Parameters ◽  
Free Energies

Phase transitions with coupled order parameters

1981 ◽  
Vol 133 (1) ◽  
pp. 103 ◽  
Author(s):  
M.A. Anisimov ◽  
E.E. Gorodetskii ◽  
V.M. Zaprudskii
Keyword(s):  
Phase Transitions ◽  
Order Parameters

AN INVESTIGATION OF THE PHASE TRANSITIONS OF A FAMILY OF PROBABILISTIC AUTOMATA

2004 ◽  
Vol 07 (01) ◽  
pp. 93-123
Author(s):  
HEINZ MÜHLENBEIN ◽  
THOMAS AUS DER FÜNTEN
Keyword(s):  
Phase Transitions ◽  
Stationary Distribution ◽  
Classification Scheme ◽  
Mean Field ◽  
Finite Size ◽  
Order Parameters ◽  
Finite Size Scaling ◽  
Probabilistic Cellular Automata ◽  
Probabilistic Automata ◽  
Major Transitions

We investigate a family of totalistic probabilistic cellular automata (PCA) which depend on three parameters. For the uniform random neighborhood and for the symmetric 1D PCA the exact stationary distribution is computed for all finite n. This result is used to evaluate approximations (uni-variate and bi-variate marginals). It is proven that the uni-variate approximation (also called mean-field) is exact for the uniform random neighborhood PCA. The exact results and the approximations are used to investigate phase transitions. We compare the results of two order parameters, the uni-variate marginal and the normalized entropy. Sometimes different transitions are indicated by the Ehrenfest classification scheme. This result shows the limitations of using just one or two order parameters for detecting and classifying major transitions of the stationary distribution. Furthermore, finite size scaling is investigated. We show that extrapolations to n=∞ from numerical calculations of finite n can be misleading in difficult parameter regions. Here, exact analytical estimates are necessary.

Statistical Mechanics: Entropy, Order Parameters, and Complexity

2021 ◽  
Author(s):  
James P. Sethna
Keyword(s):  
Statistical Mechanics ◽  
Topological Defects ◽  
Linear Response Theory ◽  
Continuous Phase ◽  
Quantum Systems ◽  
Order Parameters ◽  
Free Energies ◽  
Onset Of Chaos ◽  
The Social ◽  
Essential Insight

This text distills the core ideas of statistical mechanics to make room for new advances important to information theory, complexity, active matter, and dynamical systems. Chapters address random walks, equilibrium systems, entropy, free energies, quantum systems, calculation and computation, order parameters and topological defects, correlations and linear response theory, and abrupt and continuous phase transitions. Exercises explore the enormous range of phenomena where statistical mechanics provides essential insight — from card shuffling to how cells avoid errors when copying DNA, from the arrow of time to animal flocking behavior, from the onset of chaos to fingerprints. The text is aimed at graduates, undergraduates, and researchers in mathematics, computer science, engineering, biology, and the social sciences as well as to physicists, chemists, and astrophysicists. As such, it focuses on those issues common to all of these fields, background in quantum mechanics, thermodynamics, and advanced physics should not be needed, although scientific sophistication and interest will be important.

scholarly journals Solid-to-liquid phase transitions of sub-nanometer clusters enhance chemical transformation

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Juan-Juan Sun ◽  
Jun Cheng
Keyword(s):  
Phase Transitions ◽  
Liquid Phase ◽  
Active Sites ◽  
Catalyst Activity ◽  
Ab Initio Molecular Dynamics ◽  
Free Energies ◽  
Elementary Reactions ◽  
Au Clusters ◽  
Calculate Temperature Dependence ◽  
Entropic Effects

AbstractUnderstanding the nature of active sites is crucial in heterogeneous catalysis, and dynamic changes of catalyst structures during reaction turnover have brought into focus the dynamic nature of active sites. However, much less is known on how the structural dynamics couples with elementary reactions. Here we report an anomalous decrease in reaction free energies and barriers on dynamical sub-nanometer Au clusters. We calculate temperature dependence of free energies using ab initio molecular dynamics, and find significant entropic effects due to solid-to-liquid phase transitions of the Au clusters induced by adsorption of different states along the reaction coordinate. This finding demonstrates that catalyst dynamics can play an important role in catalyst activity.

FLUCTUATION EFFECTS IN A CLASS OF SYSTEMS WITH TWO ORDER PARAMETERS

1993 ◽  
Vol 07 (27) ◽  
pp. 1725-1731 ◽  
Author(s):  
L. DE CESARE ◽  
I. RABUFFO ◽  
D.I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Phase Transitions ◽  
Order Phase Transition ◽  
Mean Field ◽  
Ising Models ◽  
Order Parameters ◽  
The Mean ◽  
Fluctuation Effects ◽  
Second Order Phase Transition

The phase transitions described by coupled spin -1/2 Ising models are investigated with the help of the mean field and the renormalization group theories. Results for the type of possible phase transitions and their fluctuation properties are presented. A fluctuation-induced second-order phase transition is predicted.

ORDER PARAMETERS AND PHASE TRANSITIONS IN ELECTRORHEOLOGICAL FLUIDS

1992 ◽  
Vol 06 (15n16) ◽  
pp. 2635-2649 ◽  
Author(s):  
R. TAO
Keyword(s):  
Phase Transitions ◽  
Electric Fields ◽  
Lattice Structure ◽  
Reciprocal Lattice ◽  
Order Parameters ◽  
Second Phase ◽  
Two Phase ◽  
Fixed Temperature ◽  
Dielectric Spheres ◽  
Er Fluid

The ground state of an induced electrorheological (ER) solid is a body-centered tetragonal (bct) lattice with conventional Bravais vectors [Formula: see text], [Formula: see text], and [Formula: see text] where a is the radius of dielectric spheres and [Formula: see text] is the field direction. The reciprocal lattice vectors are [Formula: see text], [Formula: see text], and [Formula: see text]. Three order parameters are defined as [Formula: see text], (j = 1, 2, 3), where N is the total number of particles. Among them, ρ3 characterizes the formation of chains in the z direction, while ρ1 and ρ2 characterize the structure in the x-y plane. Monte Carlo simulations of canonical ensemble have shown that three different phases and two phase transitions exist in the ER fluid. At a fixed temperature, there are two critical electric fields Ec2 < Ec1. When the applied electric field E < Ec2, ρj (j = 1, 2, 3) are all vanishing and the ER fluid is a liquid. When Ec2 < E < Ec1, ρ1 = ρ2 = 0, but ρ3 is not vanishing, indicating that the ER fluid begins to form chains between two electrodes, but the distribution of these chains is random. This state is similar to nematic liquid crystal. The second phase transition occurs as E exceeds Ec1. Then ρ1, ρ2, and ρ3 are all non-vanishing, indicating that the chains aggregate together to form thick columns which have the bct lattice structure. These two phase transitions can also be realized at a fixed field by lowering the temperature.

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