Low temperature expansions for the Gibbs states of quantum Ising lattice systems

1984 ◽  
Vol 25 (10) ◽  
pp. 3128-3134 ◽  
Author(s):  
Lawrence E. Thomas ◽  
Zhong Yin
Keyword(s):  
Low Temperature ◽  
Gibbs States ◽  
Ising Lattice ◽  
Lattice Systems

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

Phase diagrams of lattice systems with residual entropy. II. Low temperature expansion

1989 ◽  
Vol 56 (3-4) ◽  
pp. 261-290 ◽  
Author(s):  
András Sütő ◽  
Christian Gruber ◽  
Pirmin Lemberger
Keyword(s):  
Low Temperature ◽  
Phase Diagrams ◽  
Residual Entropy ◽  
Lattice Systems ◽  
Temperature Expansion

scholarly journals SOME EXACT FORMULAE ON LONG-RANGE CORRELATION FUNCTIONS OF THE RECTANGULAR ISING LATTICE

2004 ◽  
Vol 18 (02) ◽  
pp. 275-287 ◽  
Author(s):  
SHU-CHIUAN CHANG ◽  
MASUO SUZUKI
Keyword(s):  
Correlation Function ◽  
Low Temperature ◽  
Long Range ◽  
Correlation Functions ◽  
Temperature Series ◽  
Series Expansions ◽  
Free Boundaries ◽  
Ising Lattice ◽  
Range Correlation ◽  
Exact Correlation Functions

We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free boundaries. The low-temperature series expansions of the correlation functions are presented when the spin–spin couplings are the same in both directions. The exact correlation functions can be obtained by D log Padé for the cases with simple algebraic resultant expressions. The present results show that when the two spins are infinitely far from each other, the correlation function is equal to the product of the row magnetizations of the corresponding spins, as expected. In terms of low-temperature series expansions, the approach of this m th row correlation function to the bulk correlation function for increasing m can be understood from the observation that the dominant terms of their series expansions are the same successively in the above two correlation functions. The number of these dominant terms increases monotonically as m increases.

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