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Center for Nonlinear Studies |
Recently, Gasparini et al. have examined experimentally a system of boxes etched in the surface of a wafer, each of which is filled with liquid 4He; these boxes are coupled by a supernatant film, also of liquid 4He. In the thermodynamics, there are signatures of long-range effects, for inter-box spacing out to 10,000 atomic diameters. Gasparini et al. did not offer a detailed theoretical interpretation of their findings, but instead offered the provocative view that such effects might be typical of critical systems of many types. We show that this is indeed so for uniaxial ferro-magnets and their analogues; the key ingredient is the Fisher-Privman theory of finite-size effects, a cornerstone of phase transition theory. This will be explained and examined critically in a simple system, the 2-d Ising ferromagnetic strip; contact will be made with earlier ideas of Mark Kac, a founding member of CNLS. This will then be applied to a 3-d Ising model constructed from suitably large 3-d boxes coupled together by 2-d strips, laid out on a 2-d surface. In FP theory, this becomes a network 2-d Ising model, in which the state (up or down magnetization) of each box is expressed by an Ising spin variable and the boxes are then coupled together by a pairwise ferro-magnetic interaction. We will show how this system exhibits “giant action–at-a-distance” effects which we confirmed by Monte-Carlo simulation of the original 3-d Ising system. This work was carried out at the Max Planck Institute for Intelligent Systems (abteilung Dietrich) in collaboration with Dr Anna Maciolek and Dr Oleg Vasyliev
Host: Cristiano Nisoli