Paramagnetism. Consider a system constituted by atoms located at
nodes of a lattice. Let be the total kinetic moment of atom number
in its fundamental state. It is known that to such a kinetic moment is
associated a magnetic moment given by:
where is the Bohr magneton and is the Land\'e factor. can
have only semi integer values.
Assume that the hamiltonian describing the system of atoms is:
where is the external magnetic field. What sort of particles are the
atoms in this systme, discernables or undiscernables? Find the partition
function of the system.
Study the Ising model at two dimension. Is it possible to envisage a direct
method to calculate ? Write a programm allowing to visualize the evolution
of the spins with time, temperature being a parameter.
Consider a semi--conductor metal. Free electrons of the metal are
modelized by a gas of independent fermions. The states are assumed to be
described by a sate density ,
being the nergy of a state. Give the expression of .
Find the expression binding electron number to chemical
potential. Give the expression of the potential when temperature is zero.