The distribution function PL(s) of the local order parameter s in finite blocks of size Ld is studied for Ising models for dimensionalities d=2, 3, and 4 by Monte Carlo methods. A real-space renormalization group based on phenomenological scaling yields fairly accurate results for rather small L (e.g., the standard exponents β and ν for d=3 are found as 2β/ν=1.03±0.01, 1/ν=1.60±0.05). The method can easily be generalized to arbitrary Hamiltonians, including spin dimensionalities n>1.
%0 Journal Article
%1 Binder1981Critical
%A Binder, K.
%D 1981
%I American Physical Society
%J Physical Review Letters
%K montecarlo, renormalization critical-phenomena finite-size
%N 9
%P 693--696
%R 10.1103/physrevlett.47.693
%T Critical Properties from Monte Carlo Coarse Graining and Renormalization
%U http://dx.doi.org/10.1103/physrevlett.47.693
%V 47
%X The distribution function PL(s) of the local order parameter s in finite blocks of size Ld is studied for Ising models for dimensionalities d=2, 3, and 4 by Monte Carlo methods. A real-space renormalization group based on phenomenological scaling yields fairly accurate results for rather small L (e.g., the standard exponents β and ν for d=3 are found as 2β/ν=1.03±0.01, 1/ν=1.60±0.05). The method can easily be generalized to arbitrary Hamiltonians, including spin dimensionalities n>1.
@article{Binder1981Critical,
abstract = {{The distribution function PL(s) of the local order parameter s in finite blocks of size Ld is studied for Ising models for dimensionalities d=2, 3, and 4 by Monte Carlo methods. A real-space renormalization group based on phenomenological scaling yields fairly accurate results for rather small L (e.g., the standard exponents β and ν for d=3 are found as 2β/ν=1.03±0.01, 1/ν=1.60±0.05). The method can easily be generalized to arbitrary Hamiltonians, including spin dimensionalities n>1.}},
added-at = {2019-06-10T14:53:09.000+0200},
author = {Binder, K.},
biburl = {https://www.bibsonomy.org/bibtex/262f87b7463baaa514dff9442d054a1eb/nonancourt},
citeulike-article-id = {6170526},
citeulike-linkout-0 = {http://dx.doi.org/10.1103/physrevlett.47.693},
citeulike-linkout-1 = {http://link.aps.org/abstract/PRL/v47/i9/p693},
citeulike-linkout-2 = {http://link.aps.org/pdf/PRL/v47/i9/p693},
doi = {10.1103/physrevlett.47.693},
interhash = {973055e305b33d5d6675e0ef08bdaa2e},
intrahash = {62f87b7463baaa514dff9442d054a1eb},
issn = {0031-9007},
journal = {Physical Review Letters},
keywords = {montecarlo, renormalization critical-phenomena finite-size},
month = aug,
number = 9,
pages = {693--696},
posted-at = {2011-06-21 18:43:46},
priority = {2},
publisher = {American Physical Society},
timestamp = {2019-08-01T16:16:40.000+0200},
title = {{Critical Properties from Monte Carlo Coarse Graining and Renormalization}},
url = {http://dx.doi.org/10.1103/physrevlett.47.693},
volume = 47,
year = 1981
}