1D Ising model using the Kronecker sum and Kronecker product. (1st May 2022)

• Record Type: Journal Article
• Authors: Magare, Sourabh; Roy, Abhinash Kumar; Srivastava, Varun
• Is Part Of: European journal of physics. Volume 43:Number 3(2022)
• Publication Date: 2022-05-01
• Subjects: Ising model -- Kronecker sum -- Kronecker product; Physics -- Periodicals; Physics -- Study and teaching (Higher) -- Europe -- Periodicals; 530
• DOI: 10.1088/1361-6404/ac5637
• Languages: English
• ISSNs: 0143-0807

Abstract

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