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Monte Carlo Renormalization of the 3-D-Ising Model and the Analyticity of Block-Spin Transformations

Author

Listed:
  • T.S. SMIT

    (Laboratorium voor Technische Natuurkunde, Technische Universiteit Delft, P.O. Box 5046, 2600GA Delft, The Netherlands)

  • J.R. HERINGA

    (Laboratorium voor Technische Natuurkunde, Technische Universiteit Delft, P.O. Box 5046, 2600GA Delft, The Netherlands)

  • H.W.J. BLÖTE

    (Laboratorium voor Technische Natuurkunde, Technische Universiteit Delft, P.O. Box 5046, 2600GA Delft, The Netherlands)

  • A. COMPAGNER

    (Laboratorium voor Technische Natuurkunde, Technische Universiteit Delft, P.O. Box 5046, 2600GA Delft, The Netherlands)

  • Y.T.J.C. FONK

    (Laboratorium voor Technische Natuurkunde, Technische Universiteit Delft, P.O. Box 5046, 2600GA Delft, The Netherlands)

  • A. HOOGLAND

    (Laboratorium voor Technische Natuurkunde, Technische Universiteit Delft, P.O. Box 5046, 2600GA Delft, The Netherlands)

Abstract

We present a new analysis on Monte Carlo Renormalization Group (MCRG) results obtained earlier by means of the Delft Ising System Processor (DISP). The MCRG data involve a total of 57 coupling constants, 36 even and 21 odd. Simulations were carried out for simple cubic lattices with 643, 323and 163spins.The RG transformation is assumed to be analytic. A number of relations exist between correlation functions at different renormalization levels. Some of these involve the derivatives of the stability matrix. These correlation functions enable an analysis of the so-called regular part of the RG transformation. If the Hamiltonian of the original lattice only contains nearest-neighbour couplings then the regular contributions to the specific heat and the magnetic susceptibility can be easily determined. These contributions must depend only weakly on the initial lattice size, at least if the RG transformation is analytic. We investigated whether this is indeed true when the majority-rule is applied.New simulations involving higher-order correlations will enable us to study the analytic contributions in more detail.

Suggested Citation

  • T.S. Smit & J.R. Heringa & H.W.J. Blöte & A. Compagner & Y.T.J.C. Fonk & A. Hoogland, 1991. "Monte Carlo Renormalization of the 3-D-Ising Model and the Analyticity of Block-Spin Transformations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 487-490.
    • Handle: RePEc:wsi:ijmpcx:v:02:y:1991:i:01:n:s0129183191000743
    DOI: 10.1142/S0129183191000743
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