  Calculations in Ising model can be cumbersome and non-intuitive. Here we
provide a formulation that addresses these issues for 1-D scenario. We
represent the microstates of spin interactions as a diagonal matrix. This is
done using two operations: Kronecker sum and Kronecker product. The
calculations thus become simple matter of manipulating diagonal matrices. We
address the following problems in this work: spins in the magnetic field,
open-chain 1-D Ising model, closed-chain 1-D Ising model, 1-D Ising model in an
external magnetic field. We believe that this representation will help provide
students as well as experts with a simple yet powerful technique to carry out
calculations in this model.

Statistical Mechanics