 B [**79**]{}, 69 (1990). These criteria are of a similar nature as the familiar Harris criterion, which assesses the relevance or irrelevance of random bond bulk disorder; see A. B. Harris, J. Phys. C[**7**]{}, 1671 (1974). For background on surface critical behaviour, see H. W. Diehl, in [*Phase Transitions and Critical Phenomena*]{}, edited by C. Domb and J. L. Lebowitz (Academic Press, London, 1986), Vol. 10, p. 75–267; K. Binder, in [*Phase Transitions and Critical Phenomena*]{}, edited by C. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8, p. 1-144; and H. W. Diehl, Int. J. Mod. Phys. B [**11**]{}, 3593 (1997), preprint cond-mat/9610143. S. Dietrich and H. W. Diehl, Z. Phys. B [**51**]{}, 343 (1983). H. W. Diehl, S. Dietrich, and E. Eisenriegler, Phys. Rev. B [**27**]{}, 2937 (1983). D. P. Landau and K. Binder, Phys. Rev. B [**41**]{}, 4633 (1990). C. Ruge, S. Dunkelmann, and F. Wagner, Phys. Rev. Lett. [**69**]{}, 2465 (1992). C. Ruge, S. Dunkelmann, F. Wagner, and J. Wulf, J. Stat. Phys. [**73**]{}, 293 (1992). H. W. Diehl and M. Shpot, Phys. Rev. Lett. [**73**]{}, 3431 (1994), and to be published. R. B. Griffiths, J. Math. Phys. [**8**]{}, 478 (1967); D. G. Kelly and S. Sherman, J. Math. Phys. [**9**]{}, 466 (1968). To my knowledge, not all aspects of these limiting forms have been proven in a mathematically rigorous fashion, but they are consistent with all known results. For rigorous results on the 3D semi-infinite Ising model, see J. Fr[ö]{}hlich and C.-E. Pfister, Commun. Math. Phys. [**109**]{}, 493 (1987); C.-E. Pfister and O. Penrose, Commun. Math. Phys. [**115**]{}, 691 (1988). T. W. Burkhardt and H. W. Diehl, Phys. Rev. B [**50**]{}, 3894 (1994). Cf.H. E. Stanley, [*Introduction to Phase Transitions and Critical Phenomena*]{}, [*International series of monographs on physics*]{} (Oxford University Press, Oxford, 1971), Eq. (3.2); note also that its Lemma 3 could be utilized to derive the result (\[ordeq\]) from (\[ineq\]). Quantities like