Generic replica symmetric field-theory for short range Ising spin glasses |
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Authors: | T Temesvári C De Dominicis IR Pimentel |
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Institution: | HAS Research Group for Theoretical Physics, E?tv?s University, 1117 Pázmány Péter sétány 1/A, Budapest, Hungary, HU Service de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France, FR Department of Physics and CFMC, University of Lisbon, 1649 Lisboa, Portugal, PT
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Abstract: | Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant
to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment reveals that two
different types of transitions exist, whenever the replica number n is kept larger than zero. The Sherrington-Kirkpatrick critical point in zero magnetic field between the paramagnet and replica
magnet (a replica symmetric phase with a nonzero spin glass order parameter) separates from the de Almeida-Thouless line,
along which replica symmetry breaking occurs. We argue that for studying the de Almeida-Thouless transition around the upper
critical dimension d = 6, it is necessary to use the generic cubic model with all the three bare masses and eight cubic couplings. The critical
role n may play is also emphasized. To make perturbative calculations feasible, a new representation of the cubic interaction is
introduced. To illustrate the method, we compute the masses in one-loop order. Some technical details and a list of vertex
rules are presented to help future renormalisation-group calculations.
Received 9 October 2001 |
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Keywords: | PACS 75 10 Nr Spin-glass and other random models – 05 70 Jk Critical point phenomena |
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