Searcharxiv⌕ Search

arXiv subjects

David Sherrington

Publications and source records attributed to David Sherrington.

At least 19 recordsLinked to original sources
arXiv2025

50 years of spin glass theory

In 1975, two papers were published that together sparked major new directions, conceptual, mathematical and practically applicable, in several previously disparate fields of science. In this short review, we expose key aspects of their thinking, implementations and implications, along with a selection of further crucial and consequential developments. These papers were `Theory of spin glasses' by S.F.Edwards and P.W.Anderson (EA)[1] and `Solvable Model of a Spin-Glass', by D.Sherrington and S.Kirkpatrick (SK)[2], both concerned with trying to understand recent experiments that suggested a new phase of matter.

cond-mat.dis-nn↗
arXiv2019

Materials Physics and Spin Glasses

Comparisons and analogies are drawn between materials ferroic glasses and conventional spin glasses, in terms of both experiment and theoretical modelling, with inter-system conceptual transfers leading to suggestions of further issues to investigate.

cond-mat.dis-nn↗
arXiv2018

What can spin glass theory and analogies tell us about ferroic glasses?

As well as several different kinds of periodically ordered ferroic phases, there are now recognized several different examples of ferroic glassiness, although not always described as such and in material fields of study that have mostly been developed separately. In this chapter an attempt is made to indicate common conceptual origins and features, observed or anticipated. Throughout, this aim is pursued through the use of simple models, in an attempt to determine probable fundamental origins within a larger picture of greater complication, and analogies between systems in different areas, both experimental and theoretical, in the light of significant progress in spin glass understanding.

cond-mat.mtrl-sci↗
arXiv2014

Relaxors, spin-, Stoner- and cluster-glasses

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.

cond-mat.mtrl-sci↗
arXiv2014

Ring statistics of silica bilayers

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.

cond-mat.mtrl-sci↗
arXiv2014

A spin glass perspective on ferroic glasses

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 experimental observations, without considering all possible complexities and alternatives.

cond-mat.mtrl-sci↗
arXiv2014

PMN: a minimal induced-moment soft pseudo-spin glass perspective

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.

cond-mat.mtrl-sci↗
arXiv2013

BZT:a soft pseudo-spin glass

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.

cond-mat.dis-nn↗
arXiv2013

Modeling vitreous silica bilayers

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 amorphous 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.

cond-mat.dis-nn↗
arXiv2012

Topological phase transition in complex networks

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.

cond-mat.stat-mech↗
arXiv2012

Topological phase transition in a network model with preferential attachment and node removal

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we identify a topological phase transition depending on the rate of node removal and the relative strength of preferential vs. random attachment, where the degree distribution goes from a power law to one with an exponential tail.

cond-mat.stat-mech↗
arXiv2012

Physics and Complexity: a brief spin glass perspective

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, has contributed new insights and methodologies of wide application influencing many fields of science, and has been stimulated in return.

cond-mat.dis-nn↗
arXiv2010

No spin glass phase in ferromagnetic random-field random-temperature scalar Ginzburg-Landau model

Krzakala, Ricci-Tersenghi and Zdeborova have shown recently that the random field Ising model with non-negative interactions and arbitrary external magnetic field on an arbitrary lattice does not have a static spin glass phase. In this paper we generalize the proof to a soft scalar spin version of the Ising model: the Ginzburg-Landau model with random magnetic field and random temperature-parameter. We do so by proving that the spin glass susceptibility cannot diverge unless the ferromagnetic susceptibility does.

cond-mat.dis-nn↗
arXiv2010

Quantum mechanical and information theoretic view on classical glass transitions

Using the mapping of the Fokker-Planck description of classical stochastic dynamics onto a quantum Hamiltonian, we argue that a dynamical glass transition in the former must have a precise definition in terms of a quantum phase transition in the latter. At the dynamical level, the transition corresponds to a collapse of the excitation spectrum at a critical point. At the static level, the transition affects the ground state wavefunction: while in some cases it could be picked up by the expectation value of a local operator, in others the order may be non-local, and impossible to be determined with any local probe. Here we propose instead to use concepts from quantum information theory that are not centered around local order parameters, such as fidelity and entanglement measures. We show that for systems derived from the mapping of classical stochastic dynamics, singularities in the fidelity susceptibility translate directly into singularities in the heat capacity of the classical system. In classical glassy systems with an extensive number of metastable states, we find that the prefactor of the area law term in the entanglement entropy jumps across the transition. We also discuss how entanglement measures can be used to detect a growing correlation length that diverges at the transition. Finally, we illustrate how static order can be hidden in systems with a macroscopically large number of degenerate equilibrium states by constructing a three dimensional lattice gauge model with only short-range interactions but with a finite temperature continuous phase transition into a massively degenerate phase.

cond-mat.stat-mech↗
arXiv2009

Physics and Complexity

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 the 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.

cond-mat.dis-nn↗