Thermodynamics

3. (25 pts) Consider a 3D Ising magnet, in a cubic lattice of length L. Each lattice site is occupied by a particle with either spin up or spin down. The usual rules of an Ising magnet applies: if the neighbors have the same spin, there is a favorable -e contribution to the energy. a) What are the ground states of this system (i.e. lowest energy configurations)? What are their energies? How many of them are there? b) What is an appropriate ensemble for describing the thermodynamics of this system? c) Give an expression for the entropy, S, of this system and show that this is negligible in the macroscopic (thermodynamic) limit 3. (25 pts) Consider a 3D Ising magnet, in a cubic lattice of length L. Each lattice site is occupied by a particle with either spin up or spin down. The usual rules of an Ising magnet applies: if the neighbors have the same spin, there is a favorable -e contribution to the energy. a) What are the ground states of this system (i.e. lowest energy configurations)? What are their energies? How many of them are there? b) What is an appropriate ensemble for describing the thermodynamics of this system? c) Give an expression for the entropy, S, of this system and show that this is negligible in the macroscopic (thermodynamic) limit