Consider the one-dimensional Ising model given by the following Hamiltonian:

(a) Calculate the energy E₁ of the first excited state of the system in which the spin configuration can be described in terms of a single kink, i.e. one single pair of antiparallel spins.

(b) Assume that the chain in a higher excited state can be described by a gas of noninteracting kinks distributed along the chain. Show that the partition function is given by

(c) Show that the average number of kinks 〈n〉 is given by

(d) Consider 〈l〉=N/〈n〉 to be a measure of the correlation length and derive its temperature dependence. In particular, study the limits T → 0 and T → ∞.

Transcribed Image Text:

N H=-JSS+1+NJ, i=1 with S1 for i = 1,..., N and SN+1 S1.