Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 229

b)The free energy (see Problem 4.77) then becomes

Defining and introducing a new variable we can

rewrite (S.4.100.7) in the form

Integrating (S.4.100.8) by parts, we obtain

where the 2D Debye function is

The energy is given by