Answer Happy

2. Consider a 1D string of interacting classical spins that can rotate in a plane perpendicular to the chain. The directions of unit-length spins si are described by polar angles 8¡. The interaction energy for a pair of spins is given by E = -j cos (0₁ - 0₁) KBT where j = > 0, J being the interaction constant. The Hamiltonian of the system is KBT H −h · Σ s₁ - 1 Σ si-S; Si j Sj KBT i ij where the summation is over all spins and over their nearest neighbors on the string. Here, h = µB/k³T is the reduced magnetic field, µ is the magnitude of the magnetic moment of μ individual spins, kß is the Boltzmann constant, and T is the system's temperature. This system has a phase transition into a polar ordered state. Use the mean-field approximation to calculate the critical temperature Te in vanishing field h = 0. Hint: Assume that the mean field is in the x-direction and note that near the transition the average m (si) is very small. (25) =