On a \(C^*\)-algebra approach to phase transition in the two-dimensional Ising model

DOI10.1007/BF01206017zbMath0535.46046OpenAlexW2166594857MaRDI QIDQ791114

David E. Evans, Huzihiro Araki

Publication date: 1983

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01206017

zbMATH Keywords

CAR algebraquasifree states\(Z_ 2\)-indexFermion algebraFock state of the Fermion algebraPauli spin algebraphase transition of the two-dimensional Ising modelstate on the \(C^*\)- algebra of Pauli spins on a one-dimensional latticethermodynamic limit of the Gibbs ensemble

Mathematics Subject Classification ID

Applications of selfadjoint operator algebras to physics (46L60) Quantum equilibrium statistical mechanics (general) (82B10) Miscellaneous applications of functional analysis (46N99)

Related Items (20)

A Z2-topological index as a Z2-state index ⋮ A \(\mathbb{Z}_2\)-topological index for quasi-free fermions ⋮ On a \(C^ *\)-algebra approach to phase transition in the two-dimensional Ising model. II ⋮ Locally equivalent quasifree states and index theory ⋮ Phase transitions for quantum Markov chains associated with Ising type models on a Cayley tree ⋮ Markov and stability properties of equilibrium states for nearest- neighbor interactions ⋮ Critical limit one-point correlations of monodromy fields on \({\mathbb{Z}}^ 2\) ⋮ Embeddings of U(1)-current algebras in non-commutative algebras of classical statistical mechanics ⋮ Localized endomorphisms of the chiral Ising model ⋮ Subfactors and mathematical physics ⋮ THE CHARGE QUANTUM NUMBERS OF GAUGE INVARIANT QUASI-FREE ENDOMORPHISMS ⋮ On quantum Markov chains on Cayley tree. III: Ising model ⋮ A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY-interactions on a Cayley tree ⋮ On ℤ2-indices for ground states of fermionic chains ⋮ Algebras almost commuting with Clifford algebras ⋮ Quantum Markov chains on comb graphs: Ising model ⋮ Analyticity of correlation functions for the two-dimensional Ising model ⋮ Some infinite dimensional groups and bundles ⋮ Ground states of the XY-model ⋮ Analyticity of ground states of the XY-model

Cites Work

• On the XY-model on two-sided infinite chain
• A \(C^*\)-algebra of the twodimensional Ising model
• Gibbs states of a one dimensional quantum lattice
• On quasifree states of CAR and Bogoliubov automorphisms
• A theorem on rings of operators
• Statistics of the Two-Dimensional Ferromagnet. Part I
• Crystal Statistics. II. Partition Function Evaluated by Spinor Analysis
• Crystal Statistics. III. Short-Range Order in a Binary Ising Lattice
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
• On a class of KMS states for the unitary group \(U(\infty)\)

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