Universality in the partially anisotropic three-dimensional Ising lattice
Tóm tắt
Using transfer-matrix extended phenomenological renormalization-group methods, we study the critical properties of the spin-1/2 Ising model on a simple-cubic lattice with partly anisotropic coupling strengths
$$\mathop J\limits^ \to = (J',J',J)$$
. The universality of both fundamental critical exponents y
t
and y
h
is confirmed. It is shown that the critical finite-size scaling amplitude ratios
$$U = A_{\chi ^{(4)} } A_\kappa /A_\chi ^2 ,Y_1 = A_{\kappa ''} /A_\chi$$
, and
$$Y_2 = A_{\kappa ^{(4)} } /A_{\chi ^{(4)} }$$
are independent of the lattice anisotropy parameter Δ=J′/J. For the Y
2 invariant of the three-dimensional Ising universality class, we give the first quantitative estimate Y
2≈2.013 (shape L×L×∞, periodic boundary conditions in both transverse directions).
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