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By K. H. Fischer, J. A. Hertz

The learn of spin glasses is an engaging new subject in condensed topic physics that has attracted enormous awareness over fresh years. This ebook supplies a entire account of the topic, and should supply a worthwhile assessment and connection with either newbies and specialists within the box. The authors talk about crucial advancements within the thought, experimental paintings and machine modelling of spin glasses. the 1st chapters supply a common advent to the elemental recommendations, via a dialogue of suggest box thought, the single well-established spin glass concept up to now. This ebook may be of curiosity essentially to condensed subject physicists, yet as a result of the in all likelihood huge purposes of the speculation concerned, the booklet must also attract researchers in different disciplines, together with theoretical physics, metallurgy and computational neuroscience

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Broken ergodicity and order parameters 33 fore not a suitable spin glass order parameter. Indeed, it vanishes in the limit of zero external field (at least for symmetric bond distributions, to which we restrict our attention for the moment). We clearly have to look at higher order moments. Let us consider, then, the possible kinds of second moments we obtain for the different ways of breaking ergodicity. 36) t—»oo N—»oo where the average is over a long (eventually infinitely so) set of reference times to.

E. an odd number of broken bonds), while each unfrustrated plaquette must have an even number. So if we draw (dotted) lines passing through each of the broken bonds, these lines must both enter and exit from every unfrustrated plaquette, while they must originate or terminate in frustrated plaquettes. Any spin configuration can be represented this way; its energy is given simply (relative to the ground state of the unfrustrated system) by 2 J times the total length of these 'strings'. One can of course make the same description of the configurations of an unfrustrated system.

A hint about how to resolve this apparently paradoxical situation can be got by imagining that the replica indices are real, physically meaningful indices labeling different directions in space. e. it is energetically favourable to align the magnetization along the n crystal axes, rather than in some oblique direction. In the absence of an external symmetry-breaking field, a ferromagnetic state in such a crystal could be aligned equally well along any of these axes. For a full equilibrium quantity, we must average over all these states, which will in general give different results from those for just one state.

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