Twist free energy in a spin glass |
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Authors: | E Brézin C De Dominicis |
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Institution: | (1) Laboratoire de Physique Théorique, école Normale Supérieure, 24 rue Lhomond 75231, Paris Cedex 05, France, FR;(2) Service de Physique Théorique, CE Saclay, 91191 Gif-sur-Yvette, France, FR |
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Abstract: | The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension
six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by the breaking
of reparametrization invariance of a Parisi type solution. Twisted boundary conditions are thus imposed at two opposite ends
of the system in order to study the size dependence of the twist free energy. A loop-expansion is performed to first order
around a twisted background. It is found, as expected but it is non trivial, that the theory does renormalize around such
backgrounds, as well as for the bulk. However two main differences appear, in comparison with simple ferromagnetic transitions:
(i) the loop expansion yields a (negative) anomaly in the size dependence of the free energy, thereby lifting the lower critical
dimension to a value greater than two (ii) the free energy is lowered by twisting the boundary conditions. This situation
is common in spin glasses, reflecting the non-positivity of mode multiplicity in replica symmetry breaking, but its physical
meaning is still unclear.
Received 12 April 2002 / Received in final form 30 July 2002 Published online 19 November 2002 |
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Keywords: | PACS 64 70 Pf Glass transitions – 64 60 Cn Order-disorder transformations statistical mechanics of model systems |
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