Surprising convergence of the Monte Carlo renormalization group for the three-dimensional Ising model

2017/03/07 by Dorit Ron, Achi Brandt, Robert H. Swendsen
Mathematics · Physics and Astronomy · #Block (permutation group theory) #Combinatorics #Complex Network Analysis Techniques #Condensed matter physics #Convergence (economics) #Critical exponent #Hybrid Monte Carlo #Ising model #Markov chain Monte Carlo #Mathematical physics #Mathematics #Monte Carlo method #Monte Carlo method in statistical physics #Phase transition #Physics #Quantum many-body systems #Renormalization group #Simple (philosophy) #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.95.053305

published as Phys. Rev. E 95, 053305 (2017) · 7 pages, 0 figures

arxiv created 2017/03/07 · openalex publication_date 2017/05/16 · arxiv updated 2017/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.

Citations

• Solving the 3d Ising Model with the Conformal Bootstrap II. c c -Minimization and Precise Critical Exponents
• Critical exponents of theN-vector model
• The Magnetization of the 3D Ising Model