  The field- and temperature-dependent de Haas-van Alphen oscillations spectrum
is studied for an ideal two-dimensional compensated metal whose Fermi surface
is made of a linear chain of successive orbits with electron and hole
character, coupled by magnetic breakdown. We show that the first harmonics
amplitude can be accurately evaluated on the basis of the Lifshits-Kosevich
(LK) formula by considering a set of random walks on the orbit network, in
agreement with the numerical resolution of semi-classical equations.
Oppositely, the second harmonics amplitude does not follow the LK behavior and
vanishes at a critical value of the field-to-temperature ratio which depends
explicitly on the relative value between the hole and electron effective
masses.
