Walls versus penetrable substrates

It is interesting to compare the effect of an impenetrable substrate, a wall, with the effect of a penetrable substrate. With S as in (1.28) 

It is therefore clear that the critical temperature / c depends on A, in fact / c = —logJ2gK i)gx i), and it is increasing in A. But aside for this quantitative dependence, the arguments of the previous section go through with no change and, in particular, the delocalized trajectories behave in a way that differs from the trajectory 1.7(A) only in the fact that in the 

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