1.5. Zeros of the partition function Consider a classical system with only two states of magnetization, both proportional to the volume V of the system M =±αV. In the presence of an external magnetic field B, the Hamiltonian is given by H = BM.

a. Compute the partition function in the canonical ensemble and determine its zeros in the complex plane of the temperature. Show that in the thermodynamical limit V →∞, there is an accumulation of the zeros at T =∞.

b. Compute M as a function of B and study the limit of this function when V →∞.