2004/02/25 by C. De Dominicis, Cirano De Dominicis, E. Brézin +1
Economics, Econometrics and Finance · Materials Science · Physics and Astronomy · #Complex Systems and Time Series Analysis #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2004-00264-0
arxiv created 2004/02/25 · openalex publication_date 2004/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Considering the unphysical result obtained in the calculation of the free-energy cost for twisting the boundary conditions in a spin glass, we trace it to the negative multiplicities associated with the Parisi replica-symmetry breaking (RSB). We point out that a distinct RSB, that keeps positive multiplicities, was proposed long ago, in the spirit of an ultra-long time dynamical approach due to Sompolinsky. For an homogeneous bulk system, both RSB schemes are known to yield identical free energies and observables. However, using the dynamical RSB, we have recalculated the twist free energy at the mean-field level. The free-energy cost of this twist is, as expected, positive in that scheme, as it should be.