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Renormalization group solution of the one-dimensional classical Heisenberg model

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  • Niemeijer, Th.
  • Ruijgrok, Th.W.

Abstract

It is shown that the method of Van Leeuwen1,2) and Nauenberg and Nienhuis3) in the application of the renormalization theory to Ising-like spin systems, can easily be extended to include all one-dimensional classical spin systems with nearest neighbor interactions. The series for the free energy converges very rapidly towards the known exact value (for Heisenberg interaction), provided that the temperature is not too close to the critical temperature T = 0.

Suggested Citation

  • Niemeijer, Th. & Ruijgrok, Th.W., 1975. "Renormalization group solution of the one-dimensional classical Heisenberg model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 81(3), pages 427-440.
    • Handle: RePEc:eee:phsmap:v:81:y:1975:i:3:p:427-440
    DOI: 10.1016/0378-4371(75)90057-6
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    Cited by:

    1. Ruijgrok, Th.W. & Niemeijer, Th., 1976. "The classical one-dimensional Heisenberg magnet in an external magnetic field. Transfer matrix formalism as an application of renormalization group theory “avant la lettre”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(2), pages 336-349.
    2. Rogiers, J., 1982. "Direct estimates for η from series analysis for several lattice models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 112(1), pages 303-314.

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