The hamiltonian of a one-dimensional spin-1/2 chain is written as i i where J > 0 is the interaction between the nearest neighbor sites. A finite interaction, J', between the next nearest neighbor sites also exists in this chain. (a) (10 marks) Using the mean-field theory to calculate the critical temperature, Te, below which the system spontaneously generates a finite magnetization. You may use efx = 1+x +x2/2 for small x. (b) (10 marks) Derive the magnetization near the critical temperature. (c) (10 marks) Compute the critical exponent of the magnetic field. (d) (10 marks) Can you propose a scheme that may suppress To down to zero? (e) (10 marks) Provide an interpretation for your result in (d)