Institute for Complex Systems - Sapienza - CNR

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ISC Sapienza Spin glasses

Spin glasses

Research on spin glasses

Publications >>

Spin Glasses: a brief introduction

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Spin Glasses are dilute magnetic alloys where the interactions between spins are randomly ferromagnetic or anti-ferromagnetic, and are considered as paradigmatic examples of frozen disorder. The presence of disorder (the random interactions) induces frustration and a greater difficulty for the system to find optimal configurations. As a consequence, these systems exhibit non trivial thermodynamic and dynamic properties, different and richer than those observed in their non disordered counterpart.

Spin glasses can be modeled using Ising-like Hamiltonians where the bonds between spins can be positive or negative at random. Due to the heterogeneity of the couplings, there are many triples or loops of spin sequences which are frustrated, that is for which there is no way of choosing the orientations of the spins without  frustrating at least one bond. As a consequence, even the best possible arrangement of the spins comprises for a large proportion of frustrated bonds.  More importantly, since there are many configurations with similar degree of frustration one may expect the existence of many local minima of the free energy.

Last Updated on Wednesday, 27 July 2011 12:46

Metastable states and supersymmetry

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Both the static and the dynamical behaviour occurring in mean field spin glass models models can be interpreted as consequences of the complex (free) energy landscape that spin glasses have, with many minima, valleys and saddles. Traditionally, much attention has been devoted in the past to the analysis of absolute minima, i.e. equilibrium states. More recently, we have understood that also metastable states, i.e. higher energy minima, can play an important role. In fact, for some spin glass models high energy metastable states can trap the asymptotic dynamics and determine the behaviour of the system at long times.

Last Updated on Wednesday, 27 July 2011 12:46

Field theory for finite dimensional spin glasses

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Many features predicted by mean field spin glass models, such as the behaviour of susceptibilities and correlation functions or the occurrence of aging and off-equilibrium dynamics, are qualitatively observed in experiments, suggesting that the mean field scenario may hold for finite dimensional systems also. To investigate this hypothesis a field theory for the fluctuations around the mean field solution has been developed. This theory is formally rather intricate, due to the non trivial nature of the order parameter, which is a whole function rather than simply the magnetization, as it would be in an ordinary ferromagnet.

Last Updated on Wednesday, 27 July 2011 12:46