This self-contained book is a graduate-level introduction for mathematicians and for
physicists interested in the mathematical foundations of the field, and can be used as a …

The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy
of the Sherrington-Kirkpatrick (SK) spin-glass model could have been taken as offering …

We prove the property of stochastic stability previously introduced as a consequence of the
(unproved) continuity hypothesis in the temperature of the s**lass quenched state. We …

Suitable cluster definitions have allowed researchers to describe many ordering transitions
in spin systems as geometric phenomena related to percolation. For spin glasses and some …

Presenting and develo** the theory of spin glasses as a prototype for complex systems,
this book is a rigorous and up-to-date introduction to their properties. The book combines a …

arxiv:math-ph/0505055v1 20 May 2005 Page 1 arxiv:math-ph/0505055v1 20 May 2005 the
ghirlanda-guerra identities Pierluigi Contucci†, Cristian Giardin`a‡ † Dipartimento di Matematica …

The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into
the statistical mechanics of systems with highly diversified collections of competing low …

We study a finite-range spin-glass model in arbitrary dimension, where the intensity of the
coupling between spins decays to zero over some distance γ− 1. We prove that, under a …

2.1 The ideal gas in one dimension 9 2.2 The micro-canonical ensemble 13 2.3 The
canonical ensemble and the Gibbs measure 19 2.4 Non-ideal gases in the canonical …

After introducing and discussing the link-overlap between spin configurations we show that
the Edwards–Anderson model has a replica-equivalent quenched equilibrium state, a …