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Temperature chaos is an extreme sensitivity of the equilibrium state to achange of temperature. It arises in several disordered systems that aredescribed by the so called scaling theory of spin glasses, while it seems to beabsent in mean field models. We consider a model spin glass on a tree and showthat although it has mean field behavior with replica symmetry breaking, itmanifestly has ``strong'' temperature chaos. We also show why chaos appearsonly very slowly with system size.Comment: 7 pages, 3 figures, the text is slightly change

Temperature chaos in a replica-symmetry-broken spin glass model—A hierarchical model with temperature chaos