Validity of hyperscaling for the d=3 Ising model.

Abstract

The availability of extended series expansions for 0(2)=2/H2, accurate Monte Carlo estimates of the critical temperature for the sc spin-(1/2) Ising model, and refined methods of series analysis allow the hyperscaling relation d2 - to be severely tested. From analysis of 0(2) and 0(2)/02 we estimate =1.240 0.006 and =1.565 0.004. The estimate of is in complete agreement with the prediction of hyperscaling using both the best extant series and renormalization-group estimates of the exponents and. With the assumption of hyperscaling, our analysis gives =0.630 0.002. © 1986 The American Physical Society.