Schick, together with C.E. Campbell, conducted a detailed analysis of the
phase transition in the system of
helium atoms
adsorbed on a
graphite substrate. It provided insights into the conditions for the transition, one known to exhibit the same singularities in its free energy as that of the two-dimensional three-state
Potts model. In related work, he and his colleagues enlarged the system of the q-state Potts model, in which there is a Potts spin on every lattice site that can point in q directions, to a Potts lattice gas, in which there are Potts spins only on a
fraction of the lattice sites. In doing so, they were able to employ a simple real-space
renormalization-group transformation that illuminated the reasons for the model's unusual behavior in two dimensions. For all q less than or equal to four, the Potts model exhibits an ordering transition at which the
entropy is continuous as the transition is approached from higher or lower
temperatures. There are no coexisting phases at the transition. In contrast, for all q greater than four, the transition exhibits an
entropy that is
discontinuous at the transition, i.e. obtains a different value when the transition temperature is approached from below or above. There is a
coexistence of ordered and disordered phases at the transition. The work also suggested values for
tricritical exponents of the Potts lattice gas. In 1978, he collaborated with H.J. Hilhorst and J.M.J. van Leeuwen to introduce a differential real-space
renormalization-group transformation, i.e. the lattice spacings of the two systems that were related by the transformation differed only
infinitesimally from one another. They applied it to the
two-dimensional Ising model on a triangular lattice and obtained an exact solution for the system's free
energy, one of only a few exact solutions of this model. In 1982 he collaborated with R. Pandit and M. Wortis to study the
phenomena of
adsorption of a gas on an attractive substrate as a gas to liquid transition is approached in the bulk system. There are essentially two possibilities. In one, drops of
liquid form on the surface and create a continuous film whose thickness increases without limit as the
gas to liquid transition is approached. In this case, the liquid is said to wet the substrate. In the other, drops of liquid on the surface do not spread. The bulk liquid, when it appears, must be
nucleated elsewhere than at the surface and is said not to wet the surface. M.W. Matsen and Schick elucidated the
behaviour of systems of
linear polymers consisting of alternating blocks of two different
molecules that repel one another. However, the blocks cannot separate macroscopically as they are
chemically joined. To reduce their unfavourable contacts, the system orders into various phases. The phases depend on the relative amounts of the two components. A full-phase
diagram of this system, which includes an unusual
gyroid phase, was determined. The resulting paper is the most cited of Schick's works. Schick's latest research involves the behaviour of
biological membranes. This is a subject he had considered previously in the study of the fusion of such membranes. The more recent work concerns how it could come about that the
lipid molecules that make up the
plasma membrane, rather than being distributed randomly, could form two distinct regions. They are of a characteristic size, about 100nm, and a characteristic composition. One kind of region is rich in saturated
sphingomyelin and
cholesterol, while the other is rich in
unsaturated lipids. Eschewing the commonly accepted explanation of some form of phase separation, he argued that the system's free energy is reduced if lipids with a given
intrinsic curvature go to regions of the membrane that exhibit that curvature. This leads to an
emulsion of two regions. The characteristic size is directly related to the surface tension and bending modulus of the membrane itself. ==Awards and honors==