Classification of the equilibrium states of magnets with vector and quadrupole order parameters

2007 ◽  
Vol 33 (11) ◽  
pp. 965-973 ◽  
Author(s):  
D. A. Dem’yanenko ◽  
M. Yu. Kovalevskiĭ
Keyword(s):  
Order Parameters ◽  
Equilibrium States

scholarly journals Neural-network-based order parameters for classification of binary hard-sphere crystal structures

2018 ◽  
Vol 116 (21-22) ◽  
pp. 3066-3075 ◽  
Author(s):  
Emanuele Boattini ◽  
Michel Ram ◽  
Frank Smallenburg ◽  
Laura Filion
Keyword(s):  
Neural Network ◽  
Crystal Structures ◽  
Hard Sphere ◽  
Order Parameters

Classification of continuous phase transitions and stable phases. I. Six-dimensional order parameters

1986 ◽  
Vol 33 (3) ◽  
pp. 1774-1788 ◽  
Author(s):  
Jai Sam Kim ◽  
Dorian M. Hatch ◽  
Harold T. Stokes
Keyword(s):  
Phase Transitions ◽  
Continuous Phase ◽  
Order Parameters

Classification of continuous phase transitions and stable phases. II. Four-dimensional order parameters

1986 ◽  
Vol 33 (9) ◽  
pp. 6210-6230 ◽  
Author(s):  
Jai Sam Kim ◽  
Harold T. Stokes ◽  
Dorian M. Hatch
Keyword(s):  
Phase Transitions ◽  
Continuous Phase ◽  
Order Parameters

scholarly journals Complete Classification of the Macroscopic Behavior of a Heterogeneous Network of Theta Neurons

2013 ◽  
Vol 25 (12) ◽  
pp. 3207-3234 ◽  
Author(s):  
Tanushree B. Luke ◽  
Ernest Barreto ◽  
Paul So
Keyword(s):  
Limit Cycle ◽  
Heterogeneous Network ◽  
Mean Field ◽  
Complete Classification ◽  
Field Variable ◽  
Equilibrium States ◽  
Type I ◽  
Large Network ◽  
Theta Neurons

We design and analyze the dynamics of a large network of theta neurons, which are idealized type I neurons. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global, via pulselike synapses of adjustable sharpness. Using recently developed analytical methods, we identify all possible asymptotic states that can be exhibited by a mean field variable that captures the network's macroscopic state. These consist of two equilibrium states that reflect partial synchronization in the network and a limit cycle state in which the degree of network synchronization oscillates in time. Our approach also permits a complete bifurcation analysis, which we carry out with respect to parameters that capture the degree of excitability of the neurons, the heterogeneity in the population, and the coupling strength (which can be excitatory or inhibitory). We find that the network typically tends toward the two macroscopic equilibrium states when the neuron's intrinsic dynamics and the network interactions reinforce one another. In contrast, the limit cycle state, bifurcations, and multistability tend to occur when there is competition among these network features. Finally, we show that our results are exhibited by finite network realizations of reasonable size.

On the classification of equilibrium superfluid states with scalar and tensor order parameters

2002 ◽  
Vol 28 (4) ◽  
pp. 227-234 ◽  
Author(s):  
M. Yu. Kovalevsky ◽  
S. V. Peletminsky ◽  
N. N. Chekanova
Keyword(s):  
Order Parameters ◽  
Tensor Order

Hydrodynamics

2021 ◽  
pp. 49-66
Author(s):  
Robert W. Batterman
Keyword(s):  
Correlation Functions ◽  
Linear Response ◽  
Order Parameters ◽  
Equilibrium States ◽  
Conserved Quantities ◽  
Many Body ◽  
Hydrodynamic Description ◽  
Relative Autonomy ◽  
Many Body Systems ◽  
The Continuum

This chapter begins the argument that the best way to understand the relations of relative autonomy between theories at different scales is through a mesoscale hydrodynamic description of many-body systems. It focuses on the evolution of conserved quantities of those systems in near, but out of equilibrium states. A relatively simple example is presented of a system of spins where the magnetization is the conserved quantity of interest. The chapter introduces the concepts of order parameters, of local quantities, and explains why we should be focused on the gradients of densities that inhabit the mesoscale between the scale of the continuum and that of the atomic. It introduces the importance of correlation functions and linear response.

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