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Critical Exponents Of The 3-D Ising Model

Author

Listed:
  • Rajan Gupta

    (T-8, MS-B285, Los Alamos National Laboratory, Los Alamos, NM 87545, U.S.A.)

  • Pablo Tamayo

    (T-8, MS-B285, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;
    Thinking Machines Corporation, Cambridge, MA 02143, USA)

Abstract

We present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on643,1283, and2563simple cubic lattices. Our MCRG estimates are$K_{nn}^c = 0.221655(1)(1)$andν = 0.625(1). The FSS results forKcare consistent with those from MCRG but the value of ν is not. Our best estimateη = 0.025(6)covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimateω ≈ 0.7for the correction-to-scaling exponent. We also present results for the renormalized couplinggRalong the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.

Suggested Citation

  • Rajan Gupta & Pablo Tamayo, 1996. "Critical Exponents Of The 3-D Ising Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 305-319.
    • Handle: RePEc:wsi:ijmpcx:v:07:y:1996:i:03:n:s0129183196000247
    DOI: 10.1142/S0129183196000247
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