Click here to view fulltext PDF

Permanent link:
https://www.ias.ac.in/article/fulltext/jcsc/121/05/0595-0599

Ising model; partition function, Toeplitz matrix; recurrence relation; Discrete Fourier Transform.

The partition function for one-dimensional nearest neighbour Ising models is estimated by summing all the energy terms in the Hamiltonian for N sites. The algebraic expression for the partition function is then employed to deduce the eigenvalues of the basic $2 \times 2$ matrix and the corresponding Hermitian Toeplitz matrix is derived using the Discrete Fourier Transform. A new recurrence relation pertaining to the partition function for two-dimensional Ising models in zero magnetic field is also proposed.

G Nandhini¹ M V Sangaranarayanan¹

1. Department of Chemistry, Indian Institute of Technology Madras, Chennai 600 036

Published

September 2009