scholarly journals Low temperature expansions for the Gibbs states of weakly interacting quantum Ising lattice systems

1983 ◽  
Vol 91 (3) ◽  
pp. 405-417 ◽  
Author(s):  
Lawrence E. Thomas ◽  
Zhong Yin
Keyword(s):  
Low Temperature ◽  
Gibbs States ◽  
Ising Lattice ◽  
Lattice Systems ◽  
Weakly Interacting

EUCLIDEAN GIBBS STATES OF QUANTUM LATTICE SYSTEMS

2002 ◽  
Vol 14 (12) ◽  
pp. 1335-1401 ◽  
Author(s):  
S. ALBEVERIO ◽  
YU. KONDRATIEV ◽  
YU. KOZITSKY ◽  
M. RÖCKNER
Keyword(s):  
Critical Point ◽  
Long Range ◽  
Gibbs State ◽  
Classical Model ◽  
Gibbs Measures ◽  
Gibbs States ◽  
Multiplication Operators ◽  
Approximation Technique ◽  
Lattice Systems ◽  
Euclidean Gibbs States

An approach to the description of the Gibbs states of lattice models of interacting quantum anharmonic oscillators, based on integration in infinite dimensional spaces, is described in a systematic way. Its main feature is the representation of the local Gibbs states by means of certain probability measures (local Euclidean Gibbs measures). This makes it possible to employ the machinery of conditional probability distributions, known in classical statistical physics, and to define the Gibbs state of the whole system as a solution of the equilibrium (Dobrushin–Lanford–Ruelle) equation. With the help of this representation the Gibbs states are extended to a certain class of unbounded multiplication operators, which includes the order parameter and the fluctuation operators describing the long range ordering and the critical point respectively. It is shown that the local Gibbs states converge, when the mass of the particle tends to infinity, to the states of the corresponding classical model. A lattice approximation technique, which allows one to prove for the local Gibbs states analogs of known correlation inequalities, is developed. As a result, certain new inequalities are derived. By means of them, a number of statements describing physical properties of the model are proved. Among them are: the existence of the long-range order for low temperatures and large values of the particle mass; the suppression of the critical point behavior for small values of the mass and for all temperatures; the uniqueness of the Euclidean Gibbs states for all temperatures and for the values of the mass less than a certain threshold value, dependent on the temperature.

Low-Temperature Specific Heat of CeCu2Si2and CeAl3: Coherence Effects in Kondo Lattice Systems

1984 ◽  
Vol 52 (22) ◽  
pp. 1982-1985 ◽  
Author(s):  
C. D. Bredl ◽  
S. Horn ◽  
F. Steglich ◽  
B. Lüthi ◽  
Richard M. Martin
Keyword(s):  
Low Temperature ◽  
Specific Heat ◽  
Kondo Lattice ◽  
Lattice Systems ◽  
Coherence Effects ◽  
Low Temperature Specific Heat

Microcanonical condensate fluctuations in one-dimensional weakly-interacting Bose gases

2020 ◽  
Vol 34 (35) ◽  
pp. 2050410
Author(s):  
Ji-Xuan Hou
Keyword(s):  
Number Theory ◽  
Low Temperature ◽  
Ground State ◽  
Particle Number ◽  
Microcanonical Ensemble ◽  
Bose Gases ◽  
New Approach ◽  
One Dimensional ◽  
Weakly Interacting ◽  
Counting Statistics

Weakly interacting Bose gases confined in a one-dimensional harmonic trap are studied using microcanonical ensemble approaches. Combining number theory methods, I present a new approach to calculate the particle number counting statistics of the ground state occupation. The results show that the repulsive interatomic interactions increase the ground state fraction and suppresses the fluctuation of ground state at low temperature.

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