2.2. Multiple couplings Consider the one-dimensional Ising model with N spins i =1, with the Hamiltonian given by H = J1 N1 i=1 i

2.2. Multiple couplings Consider the one-dimensional Ising model with N spins σi =±1, with the Hamiltonian given by H = −J1 N−1



i=1

σi σi+1 −J2 N−2



i=1

σiσi+2 Compute the free energy of such a system and analyse its behaviour by varying the parameters J1 and J2.

Hint. It is convenient to define τi = σiσi+1 that assume values τi =±1.