Independence of the free energy for one‐dimensional systems of fermions

1979 ◽  
Vol 20 (1) ◽  
pp. 210-215
Author(s):  
M. Campanino ◽  
G. Del Grosso
Keyword(s):  
Free Energy ◽  
One Dimensional

scholarly journals The One‐Dimensional Log‐Gas Free Energy Has a Unique Minimizer

2021 ◽  
Vol 74 (3) ◽  
pp. 615-675
Author(s):  
Matthias Erbar ◽  
Martin Huesmann ◽  
Thomas Leblé
Keyword(s):  
Free Energy ◽  
Unique Minimizer ◽  
One Dimensional ◽  
The One

Spin density wave – metal (superconductor) competition: A phase segregation scenario

2002 ◽  
Vol 12 (9) ◽  
pp. 61-64
Author(s):  
C. Pasquier ◽  
M. Héritier ◽  
D. Jérome
Keyword(s):  
Free Energy ◽  
Dispersion Relation ◽  
Fermi Level ◽  
Spin Density ◽  
Density Wave ◽  
Spin Density Wave ◽  
Phase Segregation ◽  
Organic Conductor ◽  
One Dimensional ◽  
Unique Parameter

We present a model comparing the free energy of a phase exhibiting a segregation between spin density wave (SDW) and metallic domains (eventually superconducting domains) and the free energy of homogeneous phases which explains the findings observed recently in (TMTSF)2PF6. The dispersion relation of this quasi-one-dimensional organic conductor is linearized around the Fermi level. Deviations from perfect nesting which stabilizes the SDW state are described by a unique parameter t$'_b$, this parameter can be the pressure as well.

Free-energy fluctuations in a one-dimensional random Ising system

1990 ◽  
Vol 90-91 ◽  
pp. 351-352
Author(s):  
T. Tanaka ◽  
H. Fujisaka ◽  
M. Inoue
Keyword(s):  
Free Energy ◽  
One Dimensional ◽  
Ising System

Thermal Properties of the One-Dimensional Duffin–Kemmer–Petiau Oscillator Using Hurwitz Zeta Function

2015 ◽  
Vol 70 (10) ◽  
pp. 867-874 ◽  
Author(s):  
Abdelamelk Boumali
Keyword(s):  
Free Energy ◽  
Thermal Properties ◽  
Zeta Function ◽  
Function Method ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Hurwitz Zeta Function ◽  
Expectation Value ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we investigated the thermodynamics properties of the one-dimensional Duffin–Kemmer–Petiau oscillator by using the Hurwitz zeta function method. In particular, we calculated the following main thermal quantities: the free energy, the total energy, the entropy, and the specific heat. The Hurwitz zeta function allowed us to compute the vacuum expectation value of the energy of our oscillator.

scholarly journals Weight-balanced measures and free energy for one-dimensional dynamics

1993 ◽  
Vol 5 (5) ◽  
Author(s):  
Artur O. Lopes ◽  
Wm. Douglas Withers
Keyword(s):  
Free Energy ◽  
One Dimensional

A Thermo-Magneto-Mechanical Free Energy Model for NiMnGa Single Crystals

2007 ◽  
Vol 1050 ◽  
Author(s):  
Phillip Morrison ◽  
Stefan Seelecke ◽  
Manfred Kohl ◽  
Berthold Krevet
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
Single Crystals ◽  
Energy Landscape ◽  
Stable States ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Rate Dependent ◽  
Energy Equations ◽  
Increasing Temperature

AbstractThe paper extends the authors' recent model for one-dimensional rate-dependent magneto-mechanical behavior of NiMnGa single crystals to account for temperature-dependent effects including austenite/martensite and ferro-/paramagnetic phase transitions. The magneto-mechanical model is based on the Helmholtz free energy landscape constructed for a meso-scale lattice element with strain and magnetization as order parameters. This two-dimensional energy landscape includes three paraboloidal wells representing the two easy-axis and one hard-axis martensite variants relevant for the structurally one-dimensional case. Phase transformations resulting from applied stresses and magnetic fields follow from a system of evolution laws based on the Gibbs free energy equations and the theory of thermally activated processes, which in the low-thermal-activation limit appropriately reproduce the athermal transformation behavior observed in these materials. The phase fractions subsequently determine the macroscopic strain and magnetization of a sample of NiMnGa by means of a standard averaging procedure. To account for the first-order phase transitions to austenite, additional temperature-dependent wells representing the stable states of austenitic NiMnGa are introduced into the Helmholtz energy landscape. The transition from ferromagnetic to paramagnetic states is modeled as a second order transformation based on the gradual degeneration of the ferromagnetic wells with increasing temperature.

scholarly journals Renormalization Group Approach to a One-Dimensional Cooperative T–e Jahn-Teller System

1977 ◽  
Vol 32 (1) ◽  
pp. 111-112
Author(s):  
S. Brühl ◽  
E. Sigmund
Keyword(s):  
Free Energy ◽  
Renormalization Group ◽  
Ising Model ◽  
Linear Chain ◽  
Group Approach ◽  
One Dimensional ◽  
Renormalization Group Approach ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
The One

Abstract A linear chain of T-e molecules exhibiting the cooperative Jahn-Teller effect is considered. Following Nauenberg's1 treatment of the one-dimensional Ising model a renormalization group approach is used. The series-expansion of the free energy is put into a closed form.

scholarly journals Quantum Hopfield Model

Physics ◽  
2020 ◽  
Vol 2 (2) ◽  
pp. 184-196 ◽  
Author(s):  
Masha Shcherbina ◽  
Brunello Tirozzi ◽  
Camillo Tassi
Keyword(s):  
Free Energy ◽  
Long Range ◽  
Thermodynamic Limit ◽  
Random Variables ◽  
Hopfield Model ◽  
Xy Model ◽  
One Dimensional ◽  
Random Interaction ◽  
Independent Identically Distributed

We find the free-energy in the thermodynamic limit of a one-dimensional XY model associated to a system of N qubits. The coupling among the σ i z is a long range two-body random interaction. The randomness in the couplings is the typical interaction of the Hopfield model with p patterns ( p < N ), where the patterns are p sequences of N independent identically distributed random variables (i.i.d.r.v.), assuming values ± 1 with probability 1 / 2 . We show also that in the case p ≤ α N , α ≠ 0 , the free-energy is asymptotically independent from the choice of the patterns, i.e., it is self-averaging.

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