Weak-coupling expansion for the free energy of the magneto-polaron in two dimensions

1987 ◽  
Vol 66 (4) ◽  
pp. 507-513 ◽  
Author(s):  
K. Broderix ◽  
N. Heldt ◽  
H. Leschke
Keyword(s):  
Free Energy ◽  
Weak Coupling ◽  
Two Dimensions

Weak-coupling series and the critical indices ofZpspin systems in two dimensions

1980 ◽  
Vol 22 (7) ◽  
pp. 3378-3384 ◽  
Author(s):  
C. J. Hamer ◽  
John B. Kogut
Keyword(s):  
Weak Coupling ◽  
Two Dimensions ◽  
Critical Indices

A Two-Dimensional Free Energy Model for Single Crystalline Ferroelectrics

2005 ◽  
Vol 881 ◽  
Author(s):  
Sang-Joo Kim ◽  
Stefan Seelecke ◽  
Brian L. Ball ◽  
Ralph C. Smith ◽  
Chang-Hoan Lee
Keyword(s):  
Free Energy ◽  
Evolution Equations ◽  
Saddle Points ◽  
Ferroelectric Materials ◽  
Energy Model ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Energy Potential ◽  
Single Crystalline ◽  
Free Energy Model

AbstractThe one-dimensional free energy model for ferroelectric materials developed in [1-3] is general-ized to two dimensions. The proposed two-dimensional energy potential consists of four energy wells corresponding to four variants of the material, four saddle points representing the barriers for 900 switching processes, and a local energy maximum across which 1800-switching processes take place. The free energy potential is combined with the evolution equations based on the theory of thermally activated processes. The prediction of the model is compared with the recent measurements on a Ba- TiO3 single crystalline ferroelectric in [4]. The responses of the model at various loading frequencies are calculated and the kinetics of 900 and 1800 switching processes are discussed.

The Cahn–Hilliard gradient theory for phase separation with non-smooth free energy Part I: Mathematical analysis

1991 ◽  
Vol 2 (3) ◽  
pp. 233-280 ◽  
Author(s):  
J. F. Blowey ◽  
C. M. Elliott
Keyword(s):  
Free Energy ◽  
Asymptotic Behaviour ◽  
Stationary Solution ◽  
Mathematical Analysis ◽  
Stationary Problem ◽  
Stationary Solutions ◽  
Two Dimensions ◽  
Gradient Theory ◽  
Weak Formulation ◽  
Regularity Results

A mathematical analysis is carried out for the Cahn–Hilliard equation where the free energy takes the form of a double well potential function with infinite walls. Existence and uniqueness are proved for a weak formulation of the problem which possesses a Lyapunov functional. Regularity results are presented for the weak formulation, and consideration is given to the asymptotic behaviour as the time becomes infinite. An investigation of the associated stationary problem is undertaken proving the existence of a nontrivial stationary solution and further regularity results for any stationary solution. Stationary solutions are constructed in one and two dimensions; a formula for the number of stationary solutions in one dimension is derived. It is then natural to study the asymptotic behaviour as the phenomenological parameter λ→0, the main result being that the interface between the two phases has minimal area.

3-D SPIN GLASSES AND ISING MODELS NEW METHODS ON NEW ARCHITECTURES

1993 ◽  
Vol 04 (01) ◽  
pp. 217-221
Author(s):  
GYAN BHANOT
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Ising Model ◽  
Thermodynamic Limit ◽  
Spin Glasses ◽  
Weak Coupling ◽  
Ising Models ◽  
Parallel Architectures ◽  
Strong Indication ◽  
New Methods

I describe work on 3-d Spin Glasses and the 3-d Ising Model done in collaboration with Michael Creutz at BNL and Jan Lacki at IAS Princeton. We have developed novel techniques to study these systems that make use of parallel architectures. For 3-d spin glasses, our results give strong indication that there is no phase transition in the thermodynamic limit whereas for the Ising model, we are able to extend the weak coupling expansion of the average free energy to 50 excited bonds.

scholarly journals Effective electromagnetic lagrangian at finite temperature and density in the electroweak model

Open Physics ◽  
2011 ◽  
Vol 9 (4) ◽  
Author(s):  
Andrea Erdas
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Partition Function ◽  
Field Strength ◽  
Constant Magnetic Field ◽  
Finite Temperature ◽  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Effective Coupling ◽  
Electroweak Model

AbstractUsing the exact propagators in a constant magnetic field, the effective electromagnetic lagrangian at finite temperature and density is calculated to all orders in the field strength B within the framework of the complete electroweak model, in the weak coupling limit. The partition function and free energy are obtained explicitly and the finite temperature effective coupling is derived in closed form. Some implications of this result, potentially interesting to astrophysics and cosmology, are discussed.

scholarly journals Single quark entropy and the Polyakov loop

2016 ◽  
Vol 31 (35) ◽  
pp. 1630040 ◽  
Author(s):  
Johannes Heinrich Weber
Keyword(s):  
Free Energy ◽  
Quantum Chromodynamics ◽  
Wide Temperature Range ◽  
Weak Coupling ◽  
Quantitative Result ◽  
Polyakov Loop ◽  
Crossover Region ◽  
Quark Masses ◽  
Coupling Behavior ◽  
Static Quark

We study Quantum Chromodynamics (QCD) with 2 + 1 flavors with almost physical quark masses using the highly improved staggered quark action (HISQ). We calculate the Polyakov loop in a wide temperature range, obtain the free energy and the entropy of a single static quark and discuss the QCD crossover region in detail. We show that the entropy has a peak close to the chiral crossover and consider the consequences for the deconfinement aspects of the crossover phenomena. We study the renormalized Polyakov loop susceptibilities and place them into the context of the crossover. We also obtain a quantitative result for the onset of weak-coupling behavior at high temperatures.

scholarly journals Combinatorial formulation of Ising model revisited

2003 ◽  
Vol 25 (1) ◽  
pp. 49-61 ◽  
Author(s):  
G.A.T.F.da Costa ◽  
A. L. Maciel
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Free Field ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Mathematical Relation

In 1952, Kac and Ward developed a combinatorial formulation for the two dimensional Ising model which is another method of obtaining Onsager's famous formula for the free energy per site in the termodynamic limit of the model. Feynman gave an important contribution to this formulation conjecturing a crucial mathematical relation which completed Kac and Ward ideas. In this paper, the method of Kac, Ward and Feynman for the free field Ising model in two dimensions is reviewed in a selfcontained way and Onsager's formula computed.

PATTERN FORMATION IN CHEMOTAXIC REACTION-DIFFUSION SYSTEMS

2012 ◽  
Vol 05 (03) ◽  
pp. 1260013
Author(s):  
HIROTO SHOJI ◽  
KEITARO SAITOH
Keyword(s):  
Free Energy ◽  
Pattern Formation ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Volume Filling ◽  
Reaction Diffusion Systems ◽  
Receptor Aggregation ◽  
Diffusion Systems

In this study, we investigate two-dimensional patterns generated by chemotaxis reaction-diffusion systems. We numerically examine the Keller–Segel models with the volume-filling aggregation term and the receptor aggregation term in two dimensions. Spotted, striped and reversed spotted patterns are obtained as stable motionless equilibrium patterns. The relative stability of these patterns is studied numerically on the basis of the derived free energy. The intuitive understanding of these generated patterns and the relation with three-dimensional patterns are also discussed.

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