Generalized Clifford Algebras and Spin Lattice Systems

1986 ◽  
pp. 549-554 ◽  
Author(s):  
A. K. Kwaśniewski
Keyword(s):  
Clifford Algebras ◽  
Lattice Systems ◽  
Spin Lattice

Phase transition in the Jacobsen-Stevens model of spin-lattice systems

1982 ◽  
Vol 44 (7) ◽  
pp. 1087-1090 ◽  
Author(s):  
K.C. Liu
Keyword(s):  
Phase Transition ◽  
Lattice Systems ◽  
Spin Lattice

Asymptotic expansion of the logarithm of the partition function in spin lattice systems that possess a vacuum

1989 ◽  
Vol 81 (2) ◽  
pp. 1134-1141 ◽  
Author(s):  
V. A. Arzumanyan ◽  
B. S. Nakhapetyan ◽  
S. K. Pogosyan
Keyword(s):  
Asymptotic Expansion ◽  
Partition Function ◽  
Lattice Systems ◽  
Spin Lattice

scholarly journals The Numerically Generated Series Expansions for Spin-Lattice Systems

2000 ◽  
Vol 97 (5) ◽  
pp. 901-904
Author(s):  
G. Musiał
Keyword(s):  
Series Expansions ◽  
Lattice Systems ◽  
Spin Lattice

scholarly journals EQUILIBRIUM STATISTICAL MECHANICS OF FERMION LATTICE SYSTEMS

2003 ◽  
Vol 15 (02) ◽  
pp. 93-198 ◽  
Author(s):  
HUZIHIRO ARAKI ◽  
HAJIME MORIYA
Keyword(s):  
Statistical Mechanics ◽  
Interaction Energy ◽  
Convergence Condition ◽  
Point Interaction ◽  
Translation Invariance ◽  
Major Result ◽  
Lattice Systems ◽  
Equilibrium Statistical Mechanics ◽  
Spin Lattice ◽  
The One

We study equilibrium statistical mechanics of Fermion lattice systems which require a different treatment compared with spin lattice systems due to the non-commutativity of local algebras for disjoint regions. Our major result is the equivalence of the KMS condition and the variational principle with a minimal assumption for the dynamics and without any explicit assumption on the potential. Its proof applies to spin lattice systems as well, yielding a vast improvement over known results. All formulations are in terms of a C*-dynamical systems for the Fermion (CAR) algebra [Formula: see text] with all or a part of the following assumptions: (I) The interaction is even, namely, the dynamics αt commutes with the even-oddness automorphism Θ. (Automatically satisfied when (IV) is assumed.) (II) The domain of the generator δα of αt contains the set [Formula: see text] of all strictly local elements of [Formula: see text]. (III) The set [Formula: see text] is the core of δα. (IV) The dynamics αt commutes with lattice translation automorphism group τ of [Formula: see text]. A major technical tool is the conditional expectation from [Formula: see text] onto its C*-subalgebras [Formula: see text] for any subset I of the lattice, which induces a system of commuting squares. This technique overcomes the lack of tensor product structures for Fermion systems and even simplifies many known arguments for spin lattice systems. In particular, this tool is used for obtaining the isomorphism between the real vector space of all *-derivations with their domain [Formula: see text], commuting with Θ, and that of all Θ-even standard potentials which satisfy a specific norm convergence condition for the one point interaction energy. This makes it possible to associate a unique standard potential to every dynamics satisfying (I) and (II). The convergence condition for the potential is a consequence of its definition in terms of the *-derivation and not an additional assumption. If translation invariance is imposed on *-derivations and potentials, then the isomorphism is kept and the space of translation covariant standard potentials becomes a separable Banach space with respect to the norm of the one point interaction energy. This is a crucial basis for an application of convex analysis to the equivalence proof in the major result. Everything goes in parallel for spin lattice systems without the evenness assumption (I).

Local limit theorem for the particle number in spin lattice systems

1991 ◽  
Vol 89 (2) ◽  
pp. 1138-1146 ◽  
Author(s):  
V. A. Arzumanyan ◽  
B. S. Nakhapetyan ◽  
S. K. Pogosyan
Keyword(s):  
Limit Theorem ◽  
Particle Number ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Lattice Systems ◽  
Spin Lattice

scholarly journals Exploring instantons in nonlinear sigma models with spin-lattice systems

2021 ◽  
Vol 103 (14) ◽  
Author(s):  
Sebastian Schenk ◽  
Michael Spannowsky
Keyword(s):  
Sigma Models ◽  
Lattice Systems ◽  
Spin Lattice ◽  
Nonlinear Sigma Models

scholarly journals A continuity property of the entropy density for spin lattice systems

1973 ◽  
Vol 31 (4) ◽  
pp. 291-294 ◽  
Author(s):  
M. Fannes
Keyword(s):  
Entropy Density ◽  
Continuity Property ◽  
Lattice Systems ◽  
Spin Lattice
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