Abstract
Phase transitions are fascinating physical phenomena. It is a remarkable fact that presumably short-range interactions between atoms can give rise to long-range order among them. The detailed explanation of such effects is a challenging problem in statistical mechanics. In order to simplify the problem and to provide test cases for theoretical methods, theoreticians have concentrated on model systems with low dimensionality; summations over one dimensional (1-d) or two-dimensional (2-d) spaces are usually easier than for 3-d. It has turned out that theories predict that low-dimensional systems will have special properties, rather unlike 3-d systems in many cases. The hope is that these theories can also be applied to the 3-d world. But, considering the simplifications of theories and the complications of Nature, one wonders if the theories are adequate. It seems that theorists have chosen to consider 1-d and 2-d models in order to make their work easier, but this has placed experimenters in the awkward position of trying to test the theories in a world that seems stubbornly three dimensional. Other lectures at this school have shown that it has proved possible to produce and study systems that closely resemble two-dimensional objects, in the form of films of atoms or molecules adsorbed on surfaces.
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Pomerantz, M. (1980). Studies of Literally Two-Dimensional Magnets of Manganese Stearate. In: Dash, J.G., Ruvalds, J. (eds) Phase Transitions in Surface Films. NATO Advanced Study Institutes Series, vol 51. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3057-8_10
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