Order in one dimension

Surface science now treats structures with approximately one-dimensional (1D) character, an even more constrained geometry than the nearly two-dimensional (2D) character of an interface or monolayer. Ordering in one dimension is yet more sensitive to thermal effects, but if the effective forces among the adsorbed species have long enough range the strongly correlated state survives at finite temperature. In a paper in this issue, Erwin and Hellberg propose that this is the case for the adatoms in the barium-induced Si(111) 3 x 2 reconstruction. They evaluate the interactions in the adsorbed barium with an electronic structure theory and then use the parameters for the Coulomb gas of barium ions to predict a finite temperature order/ disorder transition. Such an ambitious program is only occasionally fulfilled in other physics problems. Indeed, they make a prediction that can be tested experimentally. Some steps in their analysis probably will draw further discussion. The adsorbed barium consists of a 2D array of chains, but they find that the character of the ordering is primarily 1D and weak correlation between chains was established previously for a related surface structure. The identification of the system with an antiferromagnetic Ising model depends on the defects that disrupt the order in the chain being more discrete than continuous in nature. This also is a quantitative issue. Another model study, stimulated by adsorption on nanotube bundles, shows that (short-range) order persists in finite chains of 103 units and fragmentation arises from internal thermal excitations which pre-empt the disruption of order by simple entropic bond breaking.