Research
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. [6] 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. [7] 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. [8] 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. [9]
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. [10]
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. [11] 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. [12]
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