Abstract
Within the framework for equilibrium statistical mechanics of Fermion lattice systems formulated in our preceding work, we study the local thermodynamical stability (LTS) as an alternative characterization of equilibrium states, which works without the translation invariance assumption for the states. We propose two versions, called LTS-M (mathematical) and LTS-P (physical) according to the choice of the algebra of the outside system for a local region I, LTS-M for the commutant of the local subalgebra A(I) and LTS-P for the subalgebra A(Ic) for the complementary region Ic of I. We show that the two conditions are equivalent for even states, evenness referring to Fermion numbers. By applying known methods of proof by Sewell and Araki, the following results are obtained: (1) The LTS-M condition implies the dKMS condition for a general state φ for an arbitrary general potential (in our technical sense). The same statement holds for the LTS-P condition if φ is even. (2) The LTS-M or LTS-P condition for a translation invariant state implies that the state is a solution of the variational principle for any translation covariant standard potential.
| Original language | English |
|---|---|
| Pages (from-to) | 33-45 |
| Number of pages | 13 |
| Journal | Letters in Mathematical Physics |
| Volume | 62 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2002 Oct |
| Externally published | Yes |
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Keywords
- Equilibrium statistical mechanics
- Fermion lattice systems
- Local stability
ASJC Scopus subject areas
- Mathematical Physics
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
Cite this
Local thermodynamical stability of Fermion lattice systems. / Araki, Huzihiro; Moriya, Hajime.
In: Letters in Mathematical Physics, Vol. 62, No. 1, 10.2002, p. 33-45.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Local thermodynamical stability of Fermion lattice systems
AU - Araki, Huzihiro
AU - Moriya, Hajime
PY - 2002/10
Y1 - 2002/10
N2 - Within the framework for equilibrium statistical mechanics of Fermion lattice systems formulated in our preceding work, we study the local thermodynamical stability (LTS) as an alternative characterization of equilibrium states, which works without the translation invariance assumption for the states. We propose two versions, called LTS-M (mathematical) and LTS-P (physical) according to the choice of the algebra of the outside system for a local region I, LTS-M for the commutant of the local subalgebra A(I) and LTS-P for the subalgebra A(Ic) for the complementary region Ic of I. We show that the two conditions are equivalent for even states, evenness referring to Fermion numbers. By applying known methods of proof by Sewell and Araki, the following results are obtained: (1) The LTS-M condition implies the dKMS condition for a general state φ for an arbitrary general potential (in our technical sense). The same statement holds for the LTS-P condition if φ is even. (2) The LTS-M or LTS-P condition for a translation invariant state implies that the state is a solution of the variational principle for any translation covariant standard potential.
AB - Within the framework for equilibrium statistical mechanics of Fermion lattice systems formulated in our preceding work, we study the local thermodynamical stability (LTS) as an alternative characterization of equilibrium states, which works without the translation invariance assumption for the states. We propose two versions, called LTS-M (mathematical) and LTS-P (physical) according to the choice of the algebra of the outside system for a local region I, LTS-M for the commutant of the local subalgebra A(I) and LTS-P for the subalgebra A(Ic) for the complementary region Ic of I. We show that the two conditions are equivalent for even states, evenness referring to Fermion numbers. By applying known methods of proof by Sewell and Araki, the following results are obtained: (1) The LTS-M condition implies the dKMS condition for a general state φ for an arbitrary general potential (in our technical sense). The same statement holds for the LTS-P condition if φ is even. (2) The LTS-M or LTS-P condition for a translation invariant state implies that the state is a solution of the variational principle for any translation covariant standard potential.
KW - Equilibrium statistical mechanics
KW - Fermion lattice systems
KW - Local stability
UR - http://www.scopus.com/inward/record.url?scp=0038569439&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0038569439&partnerID=8YFLogxK
U2 - 10.1023/A:1021614924630
DO - 10.1023/A:1021614924630
M3 - Article
VL - 62
SP - 33
EP - 45
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
SN - 0377-9017
IS - 1
ER -