Subdominant critical singularities in the bcc Ising model

Shiladitya Sardar, K.G. Chakraborty

Sh. Khachatryan, A. Sedrakyan

Robert E. Shrock

Pierre Moussa

In order to analyze coalescing singularities using series expansion, a modification of the method introduced by Baker and Hunter is proposed. The Pad~ approximants on the Mellin transform are computed simultaneously for the initial series and its derivatives, allowing unbiased estimates for the critical parameters. The method is applied to the series generated by Nickel for various values of the spin in the bcc Ising model. We show that even with these longer series, the subdominant indices display large variation with the spin, and remain too small compared to the universal renormalization group prediction. However, the method does not detect other singularities in the temperature plane which are responsible for the observed discrepancy. Therefore the discrepancy is not significant.

D. Bessis, Pierre Moussa, Giorgio Turchetti

Starting from the high-temperature series for the susceptibility of the spin- 1 / 2 ferromagnetic Ising models-square, planar triangular, SC, BCC, FCC, diamond, and HSC in four, five and six dimensions-the authors analyse the analytical structure near the critical point of the susceptibility by writing it as a Laplace transform in the variable log (1-w/w c ), where w=tanh( beta J). The interest of the method is that the coalescing singularities which sit at w=w c are spread out and can be analysed separately, the first subdominant critical indices, appearing as stable poles of Pade approximants. They first recover the results for the two-dimensional models, with a high accuracy: gamma =1.74995 and gamma s =0.757. The most stable results in three dimensions are obtained for the diamond lattice: gamma =1.2506+or-0.0015 and gamma s =0.42+or-0.11. The other lattices give 0.10< gamma s <0.52. However, in all three-dimensional cases the amplitude of the subdominant singularity is less than a few per cent of the leading one. Therefore the uncertainties are large, but the subdominant singularity stays closer to the value Gamma -1=0.25 than to the field theoretical predicted one gamma s =0.75.

Michel Droz, J. Kamphorst Leal da Silva, Anna‐Sapfo Malaspinas