scholarly journals Translation invariant equilibrium states of ferromagnetic Abelian lattice systems

1982 ◽  
Vol 86 (3) ◽  
pp. 375-390 ◽  
Author(s):  
Charles-Edouard Pfister
Keyword(s):  
Equilibrium States ◽  
Invariant Equilibrium ◽  
Lattice Systems ◽  
Translation Invariant ◽  
Abelian Lattice

scholarly journals EQUILIBRIUM STATES AND THEIR ENTROPY DENSITIES IN GAUGE-INVARIANT C*-SYSTEMS

2005 ◽  
Vol 17 (04) ◽  
pp. 365-389 ◽  
Author(s):  
NOBUYUKI AKIHO ◽  
FUMIO HIAI ◽  
DÉNES PETZ
Keyword(s):  
Tensor Product ◽  
Chemical Potential ◽  
Entropy Density ◽  
Quantum Spin ◽  
Equilibrium States ◽  
Quantum Spin System ◽  
Translation Invariant ◽  
Gauge Invariant ◽  
Matrix Algebras ◽  
Kms Condition

A gauge-invariant C*-system is obtained as the fixed point subalgebra of the infinite tensor product of full matrix algebras under the tensor product unitary action of a compact group. In this paper, thermodynamics is studied in such systems and the chemical potential theory developed by Araki, Haag, Kastler and Takesaki is used. As a generalization of quantum spin system, the equivalence of the KMS condition, the Gibbs condition and the variational principle is shown for translation-invariant states. The entropy density of extremal equilibrium states is also investigated in relation to macroscopic uniformity.

scholarly journals Thermalization and Canonical Typicality in Translation-Invariant Quantum Lattice Systems

2015 ◽  
Vol 340 (2) ◽  
pp. 499-561 ◽  
Author(s):  
Markus P. Müller ◽  
Emily Adlam ◽  
Lluís Masanes ◽  
Nathan Wiebe
Keyword(s):  
Lattice Systems ◽  
Quantum Lattice ◽  
Translation Invariant ◽  
Quantum Lattice Systems ◽  
Invariant Quantum

scholarly journals Gaussian Concentration and Uniqueness of Equilibrium States in Lattice Systems

2020 ◽  
Vol 181 (6) ◽  
pp. 2131-2149
Author(s):  
J.-R. Chazottes ◽  
J. Moles ◽  
F. Redig ◽  
E. Ugalde
Keyword(s):  
Equilibrium States ◽  
Lattice Systems ◽  
Uniqueness Of Equilibrium

GLAUBER DYNAMICS FOR QUANTUM LATTICE SYSTEMS

2001 ◽  
Vol 13 (01) ◽  
pp. 51-124 ◽  
Author(s):  
S. ALBEVERIO ◽  
YU. G. KONDRATIEV ◽  
M. RÖCKNER ◽  
T. V. TSIKALENKO
Keyword(s):  
Stochastic Dynamics ◽  
Gibbs Measures ◽  
Markov Property ◽  
Glauber Dynamics ◽  
Invariant Equilibrium ◽  
Lattice Systems ◽  
Equilibrium Measures ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Gibbs Distributions

Models of quantum mechanical anharmonic lattice systems ("anharmonic crystals") are described. Temperature quantum Gibbs states are represented by classical Gibbs measures for lattice systems of loop-valued spin variables. These Gibbs measures are also obtained as invariant (equilibrium) measures of a system of stochastic differential equations ("stochastic dynamics", "stochastic quantization"). Existence and uniqueness results for these equations are established and a construction of the solution via a finite volume approximation is given. The Markov property of this solution is also exhibited and properties of the Gibbs distributions (existence, a prioiri estimates, regularity of support) are characterized in terms of the stochastic dynamics. Ergodicity and uniqueness of the Gibbs distributions are also discussed.

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