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4. 2D lattice of dipoles. In a regular 2D square lattice, there are M sites. On each lattice site there is a dipole that can only point in four directions along the bonds. In addition, the energy associated with the dipole pointing along Eî-direction is e > 0 and that along the tý-direction is 0. There is no interaction between the dipoles. (a) (5 marks) Calculate the canonical partition function of the system at temperature T. (b) (5 marks)What is the average energy per dipole? (c) (10 marks) Calculate the entropy per dipole (express your answers in terms of T). (d) (10 marks) Using micro-canonical ensemble, calculate the entropy of the system and show that it is the same as that given in (c). C Figure 2: In a two-dimensional square lattice, each lattice site is labeled by a blue dot. On the lattice site, there is a dipole that can point along either ĉ or ġ-directions, with different energies.