Critical temperatures of the d=3, s= 1 / 2 Ising model; the effect of confluent corrections to scaling

Much attention has been paid to the d=3, s=1/2 Ising model on the BCC lattice in recent years because the best high-temperature series expansions were available for this lattice. However, in order to compare series estimates of critical exponents and temperatures with independent evaluations via the Monte Carlo method, lattices of lower coordination number must be considered, since Monte Carlo studies are usually made on these. A study of extant susceptibility series on the FCC, SC, diamond and tetrahedron lattices is reported on and some comments are made on aspects of recent Monte Carlo analyses of the d=3, s=1/2 Ising model on the SC and diamond lattices.

[1]  D. Meiron,et al.  Critical Indices from Perturbation Analysis of the Callan-Symanzik Equation , 1978 .

[2]  S. McKenzie.  High-temperature reduced susceptibility of the Ising model , 1975 .

[3]  R. Gibberd.  High-temperature specific heat series of the Ising model on the crystobalite lattice , 1970 .

[4]  Dietrich Stauffer,et al.  Monte Carlo simulation of very large kinetic Ising models , 1981 .

[5]  M. .. Moore,et al.  Spin-Spin Correlation Function of the Three-Dimensional Ising Ferromagnet Above the Curie Temperature , 1969 .

[6]  A. Aharony,et al.  Universal Ratios Among Correction-to-Scaling Amplitudes and Effective Critical Exponents , 1980 .

[7]  M. Fisher,et al.  Unbiased Estimation of Corrections to Scaling by Partial Differential Approximants , 1982 .

[8]  G. A. Baker,et al.  Methods of Series Analysis. II. Generalized and Extended Methods with Application to the Ising Model , 1973 .

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

[10]  J. Rehr.  Confluent singularities and hyperscaling in the spin-1/2 Ising model , 1979 .

[11]  S. Jensen,et al.  Critical parameters for the heat capacity of three-dimensional Ising ferromagnets , 1982 .

[12]  W. J. Camp,et al.  Series analysis of corrections to scaling for the spin-pair correlations of the spin-s Ising model: Confluent singularities, universality, and hyperscaling , 1976 .

[13]  J. W. Essam,et al.  Percolation theory , 1980 .

[14]  Jean Zinn-Justin,et al.  Critical exponents from field theory , 1980 .

[15]  D. S. Gaunt,et al.  High temperature series for the susceptibility of the Ising model. II. Three dimensional lattices , 1972 .

[16]  J. Adler,et al.  New method for analyzing confluent singularities and its application to two-dimensional percolation , 1982 .

[17]  R. Swendsen,et al.  Critical behavior of the four-dimensional Ising model , 1980 .

[18]  D. Meiron,et al.  Ising Model Critical Indices in Three-Dimensions from the Callan-Symanzik Equation , 1976 .

[19]  P. Moussa.  Subdominant critical singularities in the bcc Ising model , 1982 .

[20]  P. Lepage,et al.  Analyse de la bande 2 ν4 de 12CH4 , 1979 .

[21]  T. Witten,et al.  Long-range correlations in smoke-particle aggregates , 1979 .

[22]  D. Bessis,et al.  Subdominant critical indices for the ferromagnetic susceptibility of the spin-1/2 Ising model , 1980 .

[23]  G. A. Baker,et al.  The continuous-spin Ising model, g0∶φ4∶d field theory, and the renormalization group , 1981 .

[24]  J. Adler,et al.  Unbiased map of the temperature plane and its consequences for thed=3Ising model , 1982 .

[25]  S. McKenzie.  The exponent-γ for the spin-1/2 Ising model on the face-centred cubic lattice , 1979 .

[26]  J. Felsteiner,et al.  Kadanoff block transformation by the Monte Carlo technique , 1977 .

[27]  B. Nickel.  Hyperscaling and universality in 3 dimensions , 1981 .

[28]  R. Roskies.  Reconciliation of high-temperature series and renormalization-group results by suppressing confluent singularities , 1981 .

[29]  J. Oitmaa,et al.  The Ising model on the tetrahedron lattice. I. An extended susceptibility series , 1975 .

[30]  D. S. Gaunt,et al.  Estimation of critical indices for the three-dimensional Ising model , 1973 .

[31]  G. A. Baker,et al.  A test for hyperscaling violation in the three-dimensional Ising model , 1982 .

[32]  J. Oitmaa,et al.  The critical exponent gamma for the three-dimensional Ising model , 1979 .

[33]  S. Havlin,et al.  New method of analysing self-avoiding walks in four dimensions , 1982 .

[34]  R. Roskies.  Hyperscaling in the Ising model on the simple cubic lattice , 1981 .

[35]  J. Zinn-Justin.  Analysis of high temperature series of the spin S Ising model on the body-centred cubic lattice , 1981 .