Scaling corrections: Site percolation and Ising model in three-dimensions

Using finite-size scaling techniques we obtain accurate results for critical quantities of the Ising model and the site percolation, in three dimensions. We pay special attention to parametrizing the corrections-to-scaling, which is necessary to bring the systematic errors below the statistical ones.

[1]  G. Parisi,et al.  Ising exponents in the two-dimensional site-diluted Ising model , 1997, cond-mat/9707179.

[2]  Harris,et al.  Series study of percolation moments in general dimension. , 1990, Physical review. B, Condensed matter.

[3]  Pearson,et al.  Finite-size scaling in the three-dimensional Ising model. , 1985, Physical review. B, Condensed matter.

[4]  Kenneth G. Wilson,et al.  Feynman graph expansion for critical exponents , 1972 .

[5]  Alan M. Ferrenberg,et al.  New Monte Carlo technique for studying phase transitions. , 1988, Physical review letters.

[6]  B. Nienhuis,et al.  Analytical calculation of two leading exponents of the dilute Potts model , 1982 .

[7]  University of Michigan,et al.  Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices , 1998 .

[8]  J. Adler,et al.  High and Low Temperature Series Estimates for the Critical Temperature of the 3D Ising Model , 1998 .

[9]  Rajan Gupta,et al.  CRITICAL EXPONENTS OF THE 3-D ISING MODEL , 1996 .

[10]  Measures of critical exponents in the four-dimensional site percolation , 1996, hep-lat/9612024.

[11]  F. Wegner Corrections to scaling laws , 1972 .

[12]  The four-dimensional site-diluted Ising model: A finite-size scaling study , 1997, hep-lat/9707017.

[13]  K. Wilson Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture , 1971 .

[14]  K. Wilson Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior , 1971 .

[15]  P Grassberger,et al.  Numerical studies of critical percolation in three dimensions , 1992 .

[16]  H. J. Herrmann,et al.  PRECISE DETERMINATION OF THE CONDUCTIVITY EXPONENT OF 3D PERCOLATION USING "PERCOLA" , 1996 .

[17]  Wolff,et al.  Collective Monte Carlo updating for spin systems. , 1989, Physical review letters.

[18]  G. Harris Percolation on strings and the cover-up of the c = 1 disaster , 1993, hep-th/9310137.

[19]  Peter Nightingale Finite‐size scaling and phenomenological renormalization (invited) , 1982 .

[20]  N vector spin models on the sc and the bcc lattices: A Study of the critical behavior of the susceptibility and of the correlation length by high temperature series extended to order beta(21) , 1997, hep-lat/9703018.

[21]  M. P. Nightingale,et al.  Scaling theory and finite systems , 1976 .

[22]  G. Parisi,et al.  Critical exponents of the three dimensional diluted Ising model , 1998, cond-mat/9802273.

[23]  V. Martin-Mayor,et al.  New universality class in three dimensions?: the antiferromagnetic RP2 model , 1995, hep-lat/9511003.

[24]  F. Livet The Cluster Updating Monte Carlo Algorithm Applied to the 3d Ising Problem , 1991 .

[25]  Fred Cooper,et al.  Solving φ1,24 field theory with Monte Carlo , 1982 .

[26]  Critical properties of the antiferromagnetic RP 2 model in three dimensions , 1996, hep-lat/9605037.

[27]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[28]  Giorgio Parisi,et al.  Complex zeros in the partition function of the four-dimensional SU(2) lattice gauge model , 1982 .

[29]  L. Kadanoff Scaling laws for Ising models near T(c) , 1966 .

[30]  D. Stauffer,et al.  Random Site Percolation in Three Dimensions , 1998 .

[31]  Erik Luijten,et al.  Ising universality in three dimensions: a Monte Carlo study , 1995, cond-mat/9509016.

[32]  Giorgio Parisi,et al.  Effects of the random number generator on computer simulations , 1985 .

[33]  K. Binder Finite size scaling analysis of ising model block distribution functions , 1981 .

[34]  A. L. Talapov,et al.  The magnetization of the 3D Ising model , 1996 .