Mancosu - Philosophy of Mathematical Practice (Oxford, 2008).pdf

mathematics and physics: strategies of assimilation 433orientation), so that conflict and frustration are inherent elements. A ferromagnet,in its low-temperature behaviour, exhibits spontaneous magnetization,that is to say, it exhibits a tendency for all spins to be aligned consistently. Bycontrast, a spin glass is expected to show a low-temperature phase in whichspins are randomly frozen in a disordered state.Such systems are in fact quite easy to prepare. If a dilute solution of amagnetic transition metal, such as manganese, is formed in a noble metal, suchas copper, then the ferromagnetic atoms, represented by spin variables, are sofar apart in the matrix that the dominant interaction is no longer ferromagnetic.The principal interaction force is believed to be the RKKY interaction, firststudied in the context of nuclear magnetism by Ruderman and Kittel, andlater applied to spin glasses by Kasuya and Yosida. This force oscillates betweenferromagnetic and antiferromagnetic, depending on the distance.The first indications that such alloys have unusual properties appearedin experiments of 1959 and 1960. However, the modern investigation ofthese materials really took off in the 1970s. Experiments during that decadedemonstrated that there appears to be a phase transition in such materials,exactly as for ferromagnets. In the case of spin glasses, the material does notexhibit spontaneous magnetization, but a sharp phase transition appears whenthe magnetic susceptibility is measured. The physicists interpret this as thetransition to a frozen disordered phase of the material. Furthermore, thesematerials exhibit other unusual experimental properties. For example, theydisplay relaxation and ageing effects on very extended time-scales, perhapscenturies or millenia. In this, they are analogues of ordinary glasses, whichalso show relaxation times extending over thousands of years; visitors to theEgyptian section of a museum are sometimes rewarded by the sight of a piece ofglass that is undergoing crystallization. The terminology of ‘spin glass’ originatesin this analogy. Spin glasses are to magnets as glasses are to crystals, that isto say, they are disordered magnetic materials. For more on the experimentalhistory of these unusual materials, the reader can consult chapter 15 of Fischerand Hertz (1991).These experimental discoveries led to great excitement in the community ofcondensed matter physics, as the theorists began trying to understand the spinglass phase revealed by the experiments. Part of the excitement was caused bythe fact that the properties revealed by the experiments seemed to be largelyindependent of the actual materials investigated. Spin glass states have also beenfound in magnetic insulators and amorphous alloys, where the interactions areof a completely different character (Fischer and Hertz, 1991, p.2). Thus theexperiments seemed to point to some kind of universal behaviour of disorderedsystems.