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    • Partition function of nearest neighbour Ising models: Some new insights

      G Nandhini M V Sangaranarayanan

      Volume 121 Issue 5 September 2009 pp 595-599

    • Fulltext

       

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

    • Keywords

       

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

    • Abstract

       

      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.

    • Author Affiliations

       

      G Nandhini1 M V Sangaranarayanan1

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

    • Dates

       
      Published
      September 2009

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