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On the existence of an analytic solution to the 1-D Ising model with nearest and next-nearest neighbor interactions in the presence of a magnetic field

Taherkhani, F ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1080/01411594.2010.514803
  3. Publisher: 2011
  4. Abstract:
  5. To solve the controversy, regarding the existence of an analytic solution to the 1-D Ising model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions in the presence of a magnetic field, we apply the transfer matrix method to solve the 1-D Ising model in the presence of a magnetic field, taking both NN and NNN interactions into account. We show that it is possible to write a transfer matrix only if the number of sites is even. Even in such a case, it is impossible to diagonalize the transfer matrix in an analytic form. Therefore, we employ a numerical method to obtain the eigenvalues of the transfer matrix. Moreover, the heat capacity, magnetization, and magnetic susceptibility versus temperature for different values of the competition factor (the ratio of NNN to NN interactions) are shown
  6. Keywords:
  7. Heat capacity ; Ising model ; Next-nearest interaction ; Transfer matrix ; Analytic solution ; Eigenvalues ; Heat capacities ; Nearest-neighbor interactions ; Nearest-neighbors ; Transfer matrixes ; Eigenvalues and eigenfunctions ; Magnetic fields ; Magnetic susceptibility ; Numerical methods ; Specific heat ; Transfer matrix method
  8. Source: Phase Transitions ; Volume 84, Issue 1 , Dec , 2011 , Pages 77-84 ; 01411594 (ISSN)
  9. URL: http://www.tandfonline.com./doi/abs/10.1080/01411594.2010.514803#.V2T1HxK5JIE