Abstract
The elementary excitations in a Heisenberg-Mattis random ferromagnet are studied. A solution is obtained by mapping the original problem onto a classical one, viz. determining the eigenfrequencies and eigenmodes of an isotopically disordered harmonic crystal with masses plus and minus one. The latter problem is much more amenable to an exact analysis. In contrast to previous work we find little evidence that spin waves do exist in one dimension.
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Ma, S.-K., Dasgupta, C., Hu, C.-K.: Phys. Rev. Lett.43, 1434 (1979)
Sherrington, D.: J. Phys. C10, L7 (1977)
Sherrington, D.: Phys. Rev. Lett.41, 1321 (1978)
Ching, W.Y., Leung, K.M., Huber, D.L.: Phys. Rev. Lett.39, 729 (1977)
Ching, W.Y., Huber, D.L.: Phys. Rev. B20, 4721 (1979). Note that in this work, as in [4],p=q=1/2
Mattis, D.C.: Phys. Lett. A56, 421 (1976)
Kranendonk, J. van, Vleck, J.H. van: Rev. Mod. Phys.30, 1 (1958); in particular Eqs. (82) and (83)
Chi, B.E.: Nucl. Phys. A146, 449 (1970)
Tikochinsky, J.: J. Math. Phys.20, 406 (1979)
Hemmen, J.L. van: Z. Physik B38, 271, 279 (1980)
Bellman, R.: Introduction to matrix analysis. 2nd ed., p. 108. New York: McGraw-Hill 1970
Halmos, P.R.: A Hilbert space problem book. Problem 56. Princeton NJ: Van Nostrand 1967
In a similar vein, σ(ÎD)=σ(D 1/2ÎD 1/2)⊂ℝ
Maradudin, A.A., Montroll, E.W., Weiss, G.H., Ipatova, I.P.: Theory of lattice dynamics in the harmonic approximation. 2nd ed. New York, London: Academic Press 1971
Hemmen, J.L. van: Dynamics and ergodicity of the infinite harmonic crystal. Phys. Rep.65, 43 (1980)
See Ref. [15], Chap. V—
One needs a slight modification of an ergodicity argument given in: Hemmen, J.L. van: Phys. Lett. A64, 177 (1977)
Schechter, M.: Spectra of partial differential operators. Chap. 1, Theorem 4.4. Amsterdam: North-Holland 1971
Ishii, K.: Progr. Theor. Phys. Suppl.53, 77 (1973)
Borland, R.E.: Proc. R. Soc. A274, 529 (1963)
Lieb, E.H., Mattis, D.C.: Mathematical Physics in one dimension. Chap. 2. New York, London: Academic Press 1966
Wegner, F.J.: Z. Physik B22, 273 (1975)
Kunz, H., Souillard, B.: Springer Lecture Notes in Physics Vol. 117, p. 83. Berlin, Heidelberg, New York: Springer 1980
Yoshioka, Y.: Proc. Jpn. Acad.49, 665 (1973)
Canisius, J., Hemmen, J.L. van: Manuscript in preparation
Sherrington, D.: In: Les Houches 1978 — La matière mal condensée/Ill-condensed matter. Balian, R., Maynard, R., Toulouse, G. (eds.), pp. 501–510. Amsterdam: North-Holland 1979
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van Hemmen, J.L. The mattis random magnet as an isotopically disordered harmonic crystal. Z. Physik B - Condensed Matter 40, 55–59 (1980). https://doi.org/10.1007/BF01295070
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DOI: https://doi.org/10.1007/BF01295070