Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

WORLD SCIENTIFIC eBooks

Monte Carlo and Finite-Size Scaling

Published Mar 1, 2002• 0 citations
Publisher
DOI
10.1142/9789812777935_0010

Related papers

Monte Carlo Computation of the Finite-Size Scaling Function: an Alternative Approach

Jaekwon Kim, Adauto J. F. de Souza, D. P. Landau

APS•Mar 1, 1996•0 citations

Monte Carlo Approaches to Universal Finite-Size Scaling Functions

Chin‐Kun Hu, Jau-Ann Chen, Chai‐Yu Lin +1 more

Springer proceedings in physics•Jan 1, 1998•2 citations

Comment on "Application of Finite Size Scaling to Monte Carlo Calculations"

Adrian Patrascioiu, Erhard Seiler

Physical Review Letters•Dec 12, 1994•11 citations

CRITICAL EXPONENTS OF THE 3-D ISING MODEL

Rajan Gupta, Pablo Tamayo

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 on 643, 1283, and 2563 simple cubic lattices. Our MCRG estimates are [Formula: see text] and ν = 0.625(1). The FSS results for Kc are consistent with those from MCRG but the value of ν is not. Our best estimate η = 0.025(6) covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimate ω ≈ 0.7 for the correction-to-scaling exponent. We also present results for the renormalized coupling gR along the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.

arXiv:cond-mat/9601048•International Journal of Modern Physics C•Jun 1, 1996•38 citations

Improvement of Monte Carlo estimates with covariance-optimized finite-size scaling at fixed phenomenological coupling

Francesco Parisen Toldin

In the finite-size scaling analysis of Monte Carlo data, instead of computing the observables at fixed Hamiltonian parameters, one may choose to keep a renormalization-group invariant quantity, also called phenomenological coupling, fixed at a given value. Within this scheme of finite-size scaling, we exploit the statistical covariance between the observables in a Monte Carlo simulation in order to reduce the statistical errors of the quantities involved in the computation of the critical exponents. This method is general and does not require additional computational time. This approach is demonstrated in the Ising model in two and three dimensions, where large gain factors in CPU time are obtained.

arXiv:1104.2500•Physical Review E•Aug 23, 2011•4 citations

Experiments on Finite Size Scaling

WORLD SCIENTIFIC eBooks•Jul 1, 1994•0 citations
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 on 643, 1283, and 2563 simple cubic lattices. Our MCRG estimates are [Formula: see text] and ν = 0.625(1). The FSS results for Kc are consistent with those from MCRG but the value of ν is not. Our best estimate η = 0.025(6) covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimate ω ≈ 0.7 for the correction-to-scaling exponent. We also present results for the renormalized coupling gR along the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.
In the finite-size scaling analysis of Monte Carlo data, instead of computing the observables at fixed Hamiltonian parameters, one may choose to keep a renormalization-group invariant quantity, also called phenomenological coupling, fixed at a given value. Within this scheme of finite-size scaling, we exploit the statistical covariance between the observables in a Monte Carlo simulation in order to reduce the statistical errors of the quantities involved in the computation of the critical exponents. This method is general and does not require additional computational time. This approach is demonstrated in the Ising model in two and three dimensions, where large gain factors in CPU time are obtained.