Universal ratio of magnetization moments in two-dimensional Ising models

The authors calculate the universal critical-point ratios of the square of the second and the fourth moment of the magnetization for ferromagnetic Ising models on the square and on the triangular lattices. Periodic boundary conditions are used in accordance with the four-fold and six-fold rotational symmetries of the respective lattices. These results, which are obtained by means of an analysis of finite-size data computed with a transfer-matrix technique, have an accuracy of the order of one millionth. This analysis is also applied to rectangular systems with arbitrary aspect ratios.

[1]  B. Derrida,et al.  A combination of Monte Carlo and transfer matrix methods to study 2D and 3D percolation , 1985 .

[2]  H. Blote,et al.  Accurate determination of the critical line of the square Ising antiferromagnet in a field , 1990 .

[3]  M. Fisher,et al.  Universal critical amplitudes in finite-size scaling , 1984 .

[4]  A. Compagner,et al.  The simple quadratic Ising model with crossing bonds , 1987 .

[5]  Blöte,et al.  Phase transitions in self-dual Ising models with multispin interactions and a field. , 1989, Physical Review Letters.

[6]  A D Bruce,et al.  Universal configurational structure in two-dimensional scalar models , 1988 .

[7]  M. Nightingale,et al.  Universality in two-dimensional Ising models , 1985 .

[8]  S. K. Tsang,et al.  Hard-square lattice gas , 1980 .

[9]  B. McCoy,et al.  The Two-Dimensional Ising Model , 1973 .

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

[11]  Blöte,et al.  Corrections to scaling at two-dimensional Ising transitions. , 1988, Physical review. B, Condensed matter.

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

[13]  M. Fisher,et al.  Nonlinear scaling fields and corrections to scaling near criticality , 1983 .

[14]  Burkhardt,et al.  Moments of the total magnetization and conformal invariance in the finite two-dimensional Ising model. , 1985, Physical review. B, Condensed matter.

[15]  A D Bruce,et al.  Universality in the two-dimensional continuous spin model , 1985 .