1-d Ising model using Kronecker sum and Kronecker product

Abstract: 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.