166
6 Dynamics of Quantum Mechanical Macroscopic Systems
(i) if ε and λ are arbitrary positive, then one can have:
F 1 = F 2 = 0, F 3 =
1
2
;
(6.5.31)
(ii) for 0 < 2ε < λ, one has, moreover, the possibilities:
F
2
1 + F
2
2 =
1
4
−
ε
λ
2 , F 3 =
ε
λ
.
(6.5.32)
Hence, in the case 0 < 2ε < λ, the set of ground states has similar classical picture
in su(2)
∗ as the set of τ
Q -KMS states with temperatures lying under the ‘critical
temperature’ T c . Let ω
n
0 ∈ K ∞ ⊂ S(A) corresponds to the value F ω from (6.5.31),
and let ω
s
0 be given by (6.5.26) with T = 0 and with ω
F
0 ∈ EK ∞ corresponding to
any value of F given in (6.5.32). According to [168], the thermodynamic limit of the
(unique) local ground states on A
J corresponding to the Hamiltonians Q
J coincides
with ω
s
0 .