4. A "lattice gas" consists of a lattice of N sites, each of which can be empty, in which case its energy is zero, or occupied by one particle, in which case its energy is c. Each particle has a magnetic moment of magnitude m, which in the presence of an external magnetic field H can adopt two orientations, parallel or antiparallel to the field. Therefore, in the presence of an external magnetic field, the energy at each site is either 0 or E = (c - mis), with =-1, Il. So there is a total of three energy levels corresponding to three different states. i) Find the canonical partition function for this system. ii) Evaluate the average energy and magnetization M of the system. (M = Blog Z will learn this later in the course)