2014/01/30 by Maria Chiara Angelini, Giorgio Parisi, Federico Ricci-Tersenghi +1 · 4 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Computer science #Critical dimension #Critical exponent #Ising model #Mathematical physics #Mathematics #Phase transition #Physics #Power law #Quantum mechanics #Range (aeronautics) #Renormalization group #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.stat-mech #occam
paper · pdf · doi:10.1103/physreve.89.062120
published as Phys. Rev. E 89, 062120 (2014) · 25 pages, 8 figures
arxiv created 2014/01/30 · openalex publication_date 2014/06/12 · arxiv updated 2014/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We perform a numerical study of the long-range (LR) ferromagnetic Ising model with power law decaying interactions (J∝r-d-σ) on both a one-dimensional chain (d=1) and a square lattice (d=2). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters (d,σ) to that of a short-range (SR) model in an equivalent dimension D. We then study the critical behavior of the d=2 LR model close to the lower critical σ, uncovering that the spatial correlation function decays with two different power laws: The effect of the subdominant power law is much stronger than finite-size effects and actually makes the estimate of critical exponents very subtle. By including this subdominant power law, the numerical data are consistent with the standard renormalization group (RG) prediction by Sak [Phys. Rev. B 8, 281 (1973)], thus making not necessary (and unlikely, according to Occam's razor) the recent proposal by Picco [arXiv:1207.1018] of having a new set of RG fixed points in addition to the mean-field one and the SR one.