Desai, V P

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Table 2. Pair crosa-soctions of 1.119 MeV gamma rays (millibarns per atom)518 K a o , M u rty  a n d  P a rth a sa ra d h iElomoni Expoi'imontalValueTheoreticalValue(Overbo et al 1968)C li 1 42 t o  09 1 02Zr 2 95-to . 18 2.16Rb .3 90 t o  23 2 79Sn 5.00 d-0.3 .3.43T t i 11 .40-1-0,6 O-.TPt 13.20:t0 7 0.92A n 13 40-1-0 7 7.0PI) 14.80dr0.7 7.24A c k n o w l e d g e m e n t sOne of the auihora (M.S.R.) is grateful to the C.S.I.R. Government of Tntjia, for the award of a Government Research Fellowship.R e f e r e n c e sBetho H. A. & Hoiilev W. 1934 Proo. R oy. Soc. A146, 83- Jaeger J. C. &, Hulmo, H. B. 1936 Proc. R oy. Soc. A153f 443.Oborbo T., Mork K, J. & OlHen H. A. 1968 Phya. Rev, 175, 1978.Rama Rao J. Lakshminarayana V. & Swami Jnanananda 1963 Proc. Phya. Soc. A81, 949. Yamazaki T. & Hollander J. M, 1965 Phya. Rev. 140B, 630.Indian J. Phya. 44, 518-519 (1970).Some comments on exact partition function of Ising model in Magnetism in one, two sind three dimensions in non-zero fieldB y  V . P . D e s a iSaJm Institute of Nudeur Physics, CalctUta-9 {Received 6 September 1971)In a recent paper on Ising model, Das (1970) comes to the surprising conclusion that Onsager’s (1944) and Yang’s (1952) results o f two dimensional Ising model are not reliable ! A closer look at the paper reveals that Das’s approach to the problem is basioally erroneous• The basic fallacy mSome comments on exact partition etc. 519liis approach is that he considers finite cryatah. The partition function for a finite crystal is an of temperature and as such its derivativeswill net show discontinuity (Onsager 1944^ , Wannier 1969). Hence the author does not find any phase transition in two or three dimensional finite crystals. Mere imposition of periodic boundary conditions will not ensure that the crystal is infinite. Periodic boundary conditions only eliminate the surface effects. The l orreot way to calculate exactly the partition function would be to write down the partition function and then let the juimbcr of atoms, number of rows of atoms or number of layers of atoms (depending on whether one is interested in one, two or three dimensions) go to infinity, after which only, one should try to derive the thermodynamic properties from tho partition function. This limiting pi’ocess is very complicated which requires special mathematical methods such as the matrix method or the combinatorial methods in tho caso of two and three dimensional crystals. The author is wrong in assuming that one can obtain the behaviour of one or two dimensional crystals from that of three dimensional crystals, because the three demensional problem is tho most complicated one and, therefore, as yet unsolved. There is absolutely no ground to believe that the behaviour of one, two and three dimensional crystals are similar.R efkeenobsUab 1). D., 1970 Ind. J , Phys. 44, 144 Onsager L 1944 Phys. Rev. 65, 117.Wannier G. H. 1959 Ehments o f Solid State Theory, Cambridge University Prems. Yang C N. 1952 Phy«, Rev. 85, 808.

Some Comments on Exact Partition Function of Ising Model in Magnetism in One, Two and Three Dimensions in Non-Zero Field

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Some Comments on Exact Partition Function of Ising Model in Magnetism in One, Two and Three Dimensions in Non-Zero Field

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