The width W of the active region around an active moving wall in a directed percolation process diverges at the percolation threshold pc as W ≃ Aǫ −ν ln( ǫ 0 ǫ ), with ǫ = pc − p, ǫ0 a constant, and ν = 1.734 the critical exponent of the characteristic time needed to reach the stationary state ξ ∼ ǫ −ν . The logarithmic factor arises from screening of statistically independent needle shaped sub clusters in the active region. Numerical data confirm this scaling behaviour.

A chiral four-state clock-step model is introduced to describe the deconstruction and roughening of missing-row-reconstructed (110) facets of fee crystals. Unlike simple cubic (110) facets, a reconstructed rough phase is absent. Roughening induces a simultaneous deconstruction transition, which at zero chirality has central charge c = 1.5 and both Ising and conventional roughening critical exponents. Pt(l 10) and Au(l 10) are suggested as realizations of this at small chirality, where this transition has the character of an incommensurate melting transition into a rough incommensurate missing-row fluid.PACS numbers: 64.60. Fr, 68.35.Md, 68.35.Rh, 82.65.Dp The interplay between surface reconstruction and roughening leads to intriguing new types of critical phenomena. For unreconstructed surfaces it gives rise to preroughening transitions 1,2 and for reconstructed surfaces to the roughening-induced deconstruction phase transition described in this paper. Recent experimental evidence suggests that Ni(110) and also Ar(lll) are possible realizations of preroughening. 2 " 5 The missingrow-(MR-) reconstructed (110) facets of Pt (110) and Au(llO) are being studied extensively. 6 " 9 At first the possible coupling between surface roughening and deconstruction was overlooked, and the transition was believed to be simply Ising-like. 6 Villain and Vilfan 8 pointed out that surface roughening should be expected to play a role. Indeed, the most recent experimental results for Pt(l 10) indicate the presence of step excitations. 9 First, let me point out a fundamental difference between MR reconstruction in simple-cubic (sc) and facecentered-cubic (fee) (110) facets: Fig. 1 versus Fig. 2. The MR order in Fig. 1 (a) can be characterized by an angle variable, 0=nn t , representing the two possible positions of the top rows, n t =l,2(mod2). Consider wall (a ,_rTl_n (ir.0) (b) • I • -+ -(w.-O (w>0 (c) L_ -• -FIG. 1. (a) Missing-row-reconstructed simple-cubic (110) facet, (b) with a wall excitation, and (c) with two steps.and step excitations. Walls, see Fig. 1(b), do not change the surface height, dh =0, but couple to the reconstruction, d6=*K. They have a topological charge (d0,dh) = (;r,0). Surfaces where walls are more favorable than steps, R ^Ew/Es < 1, deconstruct first and only roughen later. Steps, see Fig. 1(c), have a topological charge (d0,dh)= z (K,±\).This suggests that steps couple to both order parameters, and that surfaces with R > 1 roughen and deconstruct simultaneously. This is not so. We can disentangle the order parameters by switching the two MR labels after each step, 0-• 6 + n. A better way is to represent the MR order by parity; define Ising spins as S r =exp(i7th r ). Figure 1(c) illustrates that the antiferromagnetic spin order persists across steps, and that steps do not couple to the MR order. A sc (110) facet with R > 1 roughens first, and then enters a reconstructed rough phase, followed by an Ising deconstruction transition at a higher temperature (T). The restricted solid-on-solid (RSOS) model show...

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