Eur. Phys. J. B 25, 361-372 (2002)
https://doi.org/10.1140/epjb/e20020041

Generic replica symmetric field-theory for short range Ising spin glasses

¹ HAS Research Group for Theoretical Physics, Eötvös University, 1117 Pázmány Péter sétány 1/A, Budapest, Hungary
² Service de Physique Théorique, CEA Saclay, 91191 Gif-sur-Yvette, France
³ Department of Physics and CFMC, University of Lisbon, 1649 Lisboa, Portugal

Corresponding author: ^a temtam@helios.elte.hu

Received: 9 October 2001
Published online: 15 February 2002

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.