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David Sherrington
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In an attempt to understand the origin of relaxor ferroelectricity, it is shown that interesting behaviour of the onset of non-ergodicity and of precursor nanodomains found in first principles simulations of the relaxor alloy $mathrm {Ba(Zr}_{1-x}mathrm{Ti}_{x}mathrm{)O}_3$ can be understood easily by a simple mapping to a soft pseudo-spin glass.
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An argument that relaxor ferroelectricity in the isovalent alloy $mathrm {Ba(Zr}_{1-x}mathrm{Ti}_{x})mathrm{O}_3$ can be understood as an induced moment soft pseudo-spin glass on the B-ions of the $mathrm{ABO}_{3}$ matrix is extended to the experimentally paradigmic but theoretically more complex heterovalent relaxor $mathrm {Pb(Mg}_{1/3}mathrm{Nb}_{2/3}mathrm{)O}_3$ (PMN). It is argued that interesting behaviour of the onset of non-ergodicity, frequency-dependent susceptibility peaks and precursor nanodomains can be understood from analagous considerations of the B-ions, with the displacements of the Pb ions a largely independent, but distracting, side-feature. This contrasts with conventional conceptualizations.
Glass states of superfluid A-like phase of 3He in aerogel induced by random orientations of aerogel strands are investigated theoretically and experimentally. In anisotropic aerogel with stretching deformation two glass phases are observed. Both phases represent the anisotropic glass of the orbital ferromagnetic vector l -- the orbital glass (OG). The phases differ by the spin structure: the spin nematic vector d can be either in the ordered spin nematic (SN) state or in the disordered spin-glass (SG) state. The first phase (OG-SN) is formed under conventional cooling from normal 3He. The second phase (OG-SG) is metastable, being obtained by cooling through the superfluid transition temperature, when large enough resonant continuous radio-frequency excitation are applied. NMR signature of different phases allows us to measure the parameter of the global anisotropy of the orbital glass induced by deformation.
Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behaviour of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d<6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.
The ferromagnetic phase of an Ising model in d=3, with any amount of quenched antiferromagnetic bond randomness, is shown to undergo a transition to a spin-glass phase under sufficient quenched bond dilution. This general result, demonstrated here with the numerically exact renormalization-group solution of a d=3 hierarchical lattice, is expected to hold true generally, for the cubic lattice and for quenched site dilution. Conversely, in the ferromagnetic-spinglass-antiferromagnetic phase diagram, the spin-glass phase expands under quenched dilution at the expense of the ferromagnetic and antiferromagnetic phases. In the ferro-spinglass phase transition induced by quenched dilution reentrance is seen, as previously found for the ferro-spinglass transition induced by increasing the antiferromagnetic bond concentration.
Numerical simulations on Ising Spin Glasses show that spin glass transitions do not obey the usual universality rules which hold at canonical second order transitions. On the other hand the dynamics at the approach to the transition appear to take up a universal form for all spin glasses. The implications for the fundamental physics of transitions in complex systems are addressed.
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