Two-Level System — Schottky Anomaly
Temperature
T
:
k
B
T/ε = 1.05
Populations
E₀ = 0
p₀ = 0.50
E₁ = ε
p₁ = 0.50
Mean Energy ⟨E⟩/ε
Heat Capacity C/k
B
vs k
B
T/ε
Partition Function Z
The heat capacity peaks at
k
B
T ≈ 0.417 ε
(βε ≈ 2.399) — the Schottky anomaly. At low T the system is frozen in the ground state; at high T both levels are equally populated and C → 0.