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Replica symmetry breaking in and around six dimensions |
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| Authors: | G Parisi T Temesvári |
| Institution: | a Dipartimento di Fisica, Università di Roma “La Sapienza”, P.le Aldo Moro 2, I-00185 Roma, Italy b Statistical Mechanics and Complexity Center (SMC) — INFM — CNR, Italy c Research Group for Theoretical Physics of the Hungarian Academy of Sciences, Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary |
| Abstract: | Two, replica symmetry breaking specific, quantities of the Ising spin glass — the breakpoint x1 of the order parameter function and the Almeida-Thouless line — are calculated in six dimensions (the upper critical dimension of the replicated field theory used), and also below and above it. The results confirm that replica symmetry breaking does exist below d=6, and also the tendency of its escalation for decreasing dimension continues. As a new feature, x1 has a nonzero and universal value for d<6 at criticality. Near six dimensions we have x1c=3(6−d)+O2(6−d)]. A method to expand a generic theory with replica equivalence around the replica symmetric one is also demonstrated. |
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