The boson-fermion hybrid representation. I. Formulation: Cheng-Li Wu. Physics Department, Jilin University, Changchun, Jilin, The People's Republic of China, The Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark, and Department of Physics and Atmospheric Science, Drexel University, Philadelphia, Pennsylvania 19104; and Da Hsuan Feng, Department of Physics and Atmospheric Science, Drexel University, Philadelphia, Pennsylvania 19104
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 88 KB
- Volume
- 134
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
case it is well known) but also for the XY-model. It signals the existence of distinct surface and bulk transitions for sufficiently large values of KJK,.
For the Ising model the complete program can be carried out and the phase diagram for films of arbitrary thickness is constructed. For the double layer XY-model a sufftciently complex Migdal-style renormalization appears to be unfeasible, presumably due to the possible presence of strings between both layers. Therefore, in an alternative approach, two representations for the partition function of the double layer XY-model are given. The system can be described in terms of its topological excitations, i.e., vortices on each layer and strings, either closed or terminating in vortices, between them. The system is also written as three coupled Coulomb gases. Based on this representation a renormalization group is found, and used, together with a Griffbhs inequality for the correlation functions, to obtain information on the phase diagram. If there is a single phase transition, there is one phase where the correlations exhibit power law behavior and another where they fall off exponentially. The transition temperature increases monotonously with interlayer coupling to twice its value in two dimensions, but the nature of the phase transition for any finite inter-layer coupling appears to be different from that at zero coupling. We suggest that this is associated with the behavior of the internal strings. These results should be relevant for the renormalization of the film with isotropic bulk couplings as well as for layered systems of finite thickness, with different inter-and intra-layer couplings.
On the Meissner
Effect in Gauge Theories.