It is argued that the main characteristic features of displacive relaxor ferrolectrics of the form ${rm{A(B,B)}rm{O}}_3$ with isovalent ${rm{B,B}}$ can be explained and understood in terms of a soft-pseudospin analogue of conventional spin glasses as
extended to itinerant magnet systems. The emphasis is on conceptual comprehension and on stimulating new perspectives with respect to previous and future studies. Some suggestions are made for further studies both on actual real systems and on test model systems to probe further. The case of heterovalent systems is also considered briefly.
The recent synthesis and characterization of bilayers of vitreous silica has produced valuable new information on ring sizes and distributions. In this paper, we compare the ring statistics of experimental samples with computer generated samples. The
average ring size is fixed at six by topology, but the width, skewness and other moments of the distribution of ring edges are characteristics of particular samples. We examine the Aboav-Weaire law that quantifies the propensity of smaller rings to be adjacent to larger rings, and find similar results for available experimental samples which however differ somewhat from computer-generated bilayers currently. We introduce a new law for the areas of rings of various sizes.
A range of ferroic glasses, magnetic, polar, relaxor and strain glasses, are considered together from the perspective of spin glasses. Simple mathematical modelling is shown to provide a possible conceptual unification to back similarities of experim
ental observations, without considering all possible complexities and alternatives.
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 experimen
tally 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.
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 $mathrm {Ba(Zr}_{1-x}mat
hrm{Ti}_{x}mathrm{)O}_3$ can be understood easily by a simple mapping to a soft pseudo-spin glass.
We computer model a free-standing vitreous silica bilayer which has recently been synthesized and characterized experimentally in landmark work. Here we model the bilayer using a computer assembly procedure that starts from a single layer of amorphou
s graphene, generated using a bond switching algorithm from an initially crystalline graphene structure. Next each bond is decorated with an oxygen atom and the carbon atoms are relabeled as silicon. This monolayer can be now thought of as a two dimensional network of corner sharing triangles. Next each triangle is made into a tetrahedron, by raising the silicon atom above each triangle and adding an additional singly coordinated oxygen atom at the apex. The final step is to mirror reflect this layer to form a second layer and then attach the two layers together to form the bilayer. We show that this vitreous silica bilayer has the additional macroscopic degrees of freedom to easily form a network of identical corner sharing tetrahedra if there is a symmetry plane through the center of the bilayer going through the layer of oxygen ions that join the upper and lower layers. This has the consequence that the upper rings lie exactly above the lower rings, which are tilted in general. The assumption of a network of perfect corner sharing tetrahedra leads to a range of possible densities that we have previously characterized in three dimensional zeolites as a flexibility window. Finally, using a realistic potential, we have relaxed the bilayer to determine the density, and other structural characteristics such as the Si-Si pair distribution functions and the Si-O-Si bond angle distribution, which are compared to the experimental results obtained by direct imaging.
Preferential attachment is a central paradigm in the theory of complex networks. In this contribution we consider various generalizations of preferential attachment including for example node removal and edge rewiring. We demonstrate that generalized
preferential attachment networks can undergo a topological phase transition. This transition separates networks having a power-law tail degree distribution from those with an exponential tail. The appearance of the phase transition is closely related to the breakdown of the continuous variable description of the network dynamics.
Complex macroscopic behaviour can arise in many-body systems with only very simple elements as a consequence of the combination of competition and inhomogeneity. This paper attempts to illustrate how statistical physics has driven this recognition, h
as contributed new insights and methodologies of wide application influencing many fields of science, and has been stimulated in return.
A basis for understanding and modelling glassy behaviour in martensitic alloys and relaxor ferroelectrics is discussed from the perspective of spin glasses.
This paper is concerned with complex macroscopic behaviour arising in many-body systems through the combinations of competitive interactions and disorder, even with simple ingredients at the microscopic level. It attempts to indicate and illustrate t
he richness that has arisen, in conceptual understanding, in methodology and in application, across a large range of scientific disciplines, together with a hint of some of the further opportunities that remain to be tapped. In doing so it takes the perspective of physics and tries to show, albeit rather briefly, how physics has contributed and been stimulated.
