The Disordered Systems group at King's is at the forefront of research in statistical mechanics of disordered and complex systems.
The group covers the field of Disordered Systems in the broadest possible sense, as the study of systems of many interacting degrees of freedom, subjected to random interactions, or being immersed in a complex, chaotic or stochastic medium, and their emergent behaviours. The framework of Statistical Mechanics, both Classical and Quantum, including its far-from-equilibrium extensions, is an important unifying background for the group’s activities.
A non-exhaustive list of topics under current or past research includes studies in spin glasses and other glassy systems and associated high-dimensional random landscapes; Extreme Value Statistics for strongly correlated random variables and stochastic processes; Random Matrix Theory and its numerous applications in physics and beyond; various aspects of integrability of many-particle systems and emergent hydrodynamic behaviour, and transport phenomena in extended systems; Anderson and many-body localization, and diffusion and wave scattering in disordered and chaotic media; out-of-equilibrium fluctuations, driven systems, thermalization and pre-thermalization, and nonequilibrium thermodynamics; dynamical aspects of ecosystems, neural networks, and spectral and dynamical properties of large complex networks; interacting deterministic and stochastic systems in the context of ergodic theory; phase separation in heterogeneous mixtures such as the cytoplasm and the plasma membrane; econophysics; active matter and the physics of life, including self-propelled particles, non-reciprocal interactions, branching growth and neuronal avalanches; and fundamental and high-impact interdisciplinary questions at the interfaces between Law, Social Sciences, Data Analytics and Mathematics.
The group runs the MSc Complex Systems Modelling in collaboration with the Financial Mathematics group and the Departments of Informatics and Physics.
The group welcomes applications for post-doctoral fellowships from strong candidates, please contact the person with whom you would like to work, and see our current fellowship opportunities and how to apply.
Candidates interested in pursuing PhD studies are encouraged to contact members of the group directly to discuss potential research projects. Find out more about research degrees.
Find out more about the group on the Disordered Systems external website.
Themes

Disordered Systems Research
The research activities of the group concentrate on the analysis and development of mathematical theories and models with which to describe the statics and dynamics of disordered (or `complex') systems in physics, biology, financial markets, and computer science. Such systems are characterized by microscopic (usually stochastic) dynamic elements with mutual interactions without global regularity but with a significant degree of built-in competition and incompatibility, resulting in the existence of many locally stable states for the system as a whole and a highly non-ergodic `glassy' type of dynamics.

PINs
The definition and generation of good null models to assess the statistical relevance of observed features in protein interaction networks (PIN) is a well known problem in systems biology, where the aim is to understand how the structure of PINs relates to their biological functionality. By using statistical mechanics techniques, Annibale and Coolen recently derived explicit formulae for complex network ensembles with built-in topologies beyond the degrees, as proxies for real networks; provided exact algorithms for generating random graphs from such ensembles; and derived information-theoretic tools to quantify distances between networks. The application of these tools has enabled them and their coworkers to quantify detection biases in PIN data sets and species consistency.

Physical Systems
In the domain of physical systems, the question of how to pack spheres optimally is familiar from everyday examples such as a greengrocer's stack of oranges. But what if the spheres have a range of sizes, as happens for example in colloidal suspensions? Controversy has surrounded this issue, with proposals that the optimal structure could be disordered. Sollich and co-workers have recently provided a definitive answer, combining mathematical theory (polydisperse phase equilibrium calculations) with specialized numerical simulation techniques. The optimal structures are ordered, i.e. crystalline solids, but depending on the density and the spread of particle sizes the system will fractionate: the particles are effectively sorted out into several solid phases, with each containing only a small range of particle sizes.

Universal Glassy Low-Temperature Anomalies
Kuehn has provided the first formulation of a microscopic model to describe the emergence of the universal glassy low-temperature anomalies, including an understanding of the origin of the mysterious so-called quantitative universality -- a problem that had been open since its formulation in the late 80s. He has also given the first proper formulation and analysis of the role of interactions (networks of functional dependencies) on operational and credit risk, including recently an analysis of the influence of credit derivatives on systemic risk.

Sparse Symmetric Random Matrices
A collaboration between group members Kuehn and Perez Castillo and international collaborators also led to a breakthrough in the spectral problem for sparse symmetric random matrices, allowing to efficiently compute spectral densities of such systems in the limit of large matrix size to any desired accuracy -- more than 20 years after a solution to this problem was first attempted.
Publications
Activities

Tiziana Di Matteo successfully secures funding from Jupiter Asset Management Ltd. for a PhD studentship
Joseph Bradley has now joined KCL, starting his PhD in Econophysics, working with the Systematic Equities Team at Jupiter Asset Management. Joseph and the team are looking at how Econophysics can help the team to understand and manage their portfolios better.

Recent Publishing Success with Papers on Ergodicity
Members of the Disordered Systems group have recently published two papers about 'ergodicity'. Ergodicity is a fundamental concept, which says that, in certain situations, averaging over time is equivalent to averaging over a statistical ensemble. It is at the basis of much of statistical physics, but rigorous results on the presence or absence of ergodicity in many-body systems such as quantum chains and lattices are rare. (1) François Huveneer published a paper in Physics A about “Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain“ with V. De Roeck, B Meeus, and O Prośniak. They provide a brief introduction to the breaking of ergodicity in disordered systems. In particular they prove a simple but original and rigorous result about the lack of ergodicity in a strongly disordered quantum chain, by exhibiting explicitly a full set of quasi-local conserved quantities, thus clarifying this basic concept of the physics of disordered systems. (2) Prof. Benjamin Doyon and his student Dimitrios Ampelogiannis have a paper “Almost everywhere ergodicity in quantum lattice models” accepted for publication in Communications in Mathematical Physics, the most high-profile journal of mathematical physics. They consider ergodicity under averaging not just over time, but over some straight path in space-time at velocity v. They show that in every possible translation-invariant (non-disordered) cubic quantum lattices, and for almost every v, there is indeed ergodicity. This is the first such general rigorous result for ergodicity in quantum lattices and opens the door for new rigorous avenues towards related fundamental questions such as thermalisation and hydrodynamics.

Tiziana Di Matteo Gives Keynote Speech at Conference on Complex Systems 2023 in Brazil
Tiziana Di Matteo gave a keynote talk, “A dive into the complexity of financial time series: progress and challenge by means of scaling analysis” at the Conference on Complex Systems 2023 in Brazil on 16 October 2023. This is a major event of the Complex System Society.

Advanced Lectures Series
The Disordered Systems group is hosting an Advanced Lectures series for PhD students, postdocs and all who want to attend and learn about advanced topics in the area of classical and quantum statistical mechanics of disordered and complex systems. These are lectures given by group members as well as visitors, in particular from the Distinguished Visitor series of the Maths Department. As part of this, Prof. Leonid Pastur delivered four very-well attended lectures on the subject of 'Quantum Entanglement in Disordered Systems.'

Journal of Statistical Mechanics Article Selected for Highlights Collection
Congratulations to Prof. Doyon (Department of Mathematics) and his collaborators, whose article 'Correlation functions and transport coefficients in generalised hydrodynamics' has been highlighted as part of the collection of noteworthy articles by the Scientific Directors from the articles published in JSTAT in recent months.

Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths
An article by Prof. Doyon and his student Dimitrios Ampelogiannis (Department of Mathematics) has been published in Annales Henri Poincaré, in a special issue dedicated to the memory of well-known mathematical physicist Krzysztof Gawedski. The article, entitled ' Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths' can be viewed via the below link.

Article published in Journal of Physics A
A recent article, 'Hydrodynamic gauge fixing and higher order hydrodynamic expansion' by Prof. Doyon (Department of Mathematics) and his collaborator has been published in the Journal of Physics.
.x937f4972.jpg?width=380&height=215&fit=crop&f=webp)
Reimer Kühn Appointed to Scientific Advisory Board
Congratulations to Reimer Kühn who has been appointed as a member of the Scientific Advisory Board for the Bielefeld Center for Interdisciplinary Research (ZiF) for a four-year tenure starting from October 2022.

'Physical Review E' Editorial Board Member Invitation
Congratulations to Izaak Neri, from the Disordered Systems Group in the Mathematics Department, who has been invited to be an editorial board member for the well-recognised journal, 'Physical Review E' (for the period of 2023-2025) of the American Physical Society.

Proceedings of Machine Learning Research Publication
In July 2022, the paper 'Fluctuations, Bias, Variance & Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension', co-authored by Gabriele Sicuro from the Disordered Systems Group at the Mathematics Department, was published in the prestigious international journal, Proceedings of Machine Learning Research. This was published in conjunction with the 39th International Conference on Machine Learning.

MECO47
Gabriele Sicuro and Pierpaolo Vivo from the Disordered Systems Group in the Mathematics Department, along with colleagues from UCL and IPhT Paris, organised the MECO47 in June 2022. MECO47 marked the 47th conference of the Middle European Cooperation in Statistical Physics (a famous international conference series in Statistical Physics). The hybrid event was held in Erice, Sicily from 12 June 2022 - 16 June 2022. There was a strong presence of the group at the conference, with Paola Ruggiero and Reimer Kuehn as speakers.
News
New framework uses games of chance to put 'price' on intangible assets
The new statistical model could have major implications for how data is bought and sold

Maths Professor at King's awarded top Institute of Physics prize for theoretical physics
Professor Benjamin Doyon received the 2022 John William Strutt, Lord Rayleigh Medal and Prize

King's women in maths: Tiziana Di Matteo
Tiziana Di Matteo interview

New graph-based visualisation interface for UK laws
New visualisation platform developed at King’s makes it easier to work with complex legal texts.

Events

Disordered Systems Days at King's College London
The Disordered Systems Group at King's College London are hosting a two-day event on the physics of disorder.
Please note: this event has passed.

Pointwise Ergodic Theory & Connections Conference
This is a conference about Pointwise Ergodic Theory, Discrete Harmonic Analysis and their connections, organised by Ben Krause, from the Department of...
Please note: this event has passed.
Seminars
The Disordered Systems group has a regular weekly informal seminar, usually held at 12:00 on Mondays.
The group also invites visitors to give seminars on Wednesday.
For more information, please email the seminar organiser, Matteo Tanzi on matteo.tanzi@kcl.ac.uk
The group also hosts an advanced lecture series, see https://dsadvancedlectures.weebly.com/ for information"
Themes

Disordered Systems Research
The research activities of the group concentrate on the analysis and development of mathematical theories and models with which to describe the statics and dynamics of disordered (or `complex') systems in physics, biology, financial markets, and computer science. Such systems are characterized by microscopic (usually stochastic) dynamic elements with mutual interactions without global regularity but with a significant degree of built-in competition and incompatibility, resulting in the existence of many locally stable states for the system as a whole and a highly non-ergodic `glassy' type of dynamics.

PINs
The definition and generation of good null models to assess the statistical relevance of observed features in protein interaction networks (PIN) is a well known problem in systems biology, where the aim is to understand how the structure of PINs relates to their biological functionality. By using statistical mechanics techniques, Annibale and Coolen recently derived explicit formulae for complex network ensembles with built-in topologies beyond the degrees, as proxies for real networks; provided exact algorithms for generating random graphs from such ensembles; and derived information-theoretic tools to quantify distances between networks. The application of these tools has enabled them and their coworkers to quantify detection biases in PIN data sets and species consistency.

Physical Systems
In the domain of physical systems, the question of how to pack spheres optimally is familiar from everyday examples such as a greengrocer's stack of oranges. But what if the spheres have a range of sizes, as happens for example in colloidal suspensions? Controversy has surrounded this issue, with proposals that the optimal structure could be disordered. Sollich and co-workers have recently provided a definitive answer, combining mathematical theory (polydisperse phase equilibrium calculations) with specialized numerical simulation techniques. The optimal structures are ordered, i.e. crystalline solids, but depending on the density and the spread of particle sizes the system will fractionate: the particles are effectively sorted out into several solid phases, with each containing only a small range of particle sizes.

Universal Glassy Low-Temperature Anomalies
Kuehn has provided the first formulation of a microscopic model to describe the emergence of the universal glassy low-temperature anomalies, including an understanding of the origin of the mysterious so-called quantitative universality -- a problem that had been open since its formulation in the late 80s. He has also given the first proper formulation and analysis of the role of interactions (networks of functional dependencies) on operational and credit risk, including recently an analysis of the influence of credit derivatives on systemic risk.

Sparse Symmetric Random Matrices
A collaboration between group members Kuehn and Perez Castillo and international collaborators also led to a breakthrough in the spectral problem for sparse symmetric random matrices, allowing to efficiently compute spectral densities of such systems in the limit of large matrix size to any desired accuracy -- more than 20 years after a solution to this problem was first attempted.
Publications
Activities

Tiziana Di Matteo successfully secures funding from Jupiter Asset Management Ltd. for a PhD studentship
Joseph Bradley has now joined KCL, starting his PhD in Econophysics, working with the Systematic Equities Team at Jupiter Asset Management. Joseph and the team are looking at how Econophysics can help the team to understand and manage their portfolios better.

Recent Publishing Success with Papers on Ergodicity
Members of the Disordered Systems group have recently published two papers about 'ergodicity'. Ergodicity is a fundamental concept, which says that, in certain situations, averaging over time is equivalent to averaging over a statistical ensemble. It is at the basis of much of statistical physics, but rigorous results on the presence or absence of ergodicity in many-body systems such as quantum chains and lattices are rare. (1) François Huveneer published a paper in Physics A about “Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain“ with V. De Roeck, B Meeus, and O Prośniak. They provide a brief introduction to the breaking of ergodicity in disordered systems. In particular they prove a simple but original and rigorous result about the lack of ergodicity in a strongly disordered quantum chain, by exhibiting explicitly a full set of quasi-local conserved quantities, thus clarifying this basic concept of the physics of disordered systems. (2) Prof. Benjamin Doyon and his student Dimitrios Ampelogiannis have a paper “Almost everywhere ergodicity in quantum lattice models” accepted for publication in Communications in Mathematical Physics, the most high-profile journal of mathematical physics. They consider ergodicity under averaging not just over time, but over some straight path in space-time at velocity v. They show that in every possible translation-invariant (non-disordered) cubic quantum lattices, and for almost every v, there is indeed ergodicity. This is the first such general rigorous result for ergodicity in quantum lattices and opens the door for new rigorous avenues towards related fundamental questions such as thermalisation and hydrodynamics.

Tiziana Di Matteo Gives Keynote Speech at Conference on Complex Systems 2023 in Brazil
Tiziana Di Matteo gave a keynote talk, “A dive into the complexity of financial time series: progress and challenge by means of scaling analysis” at the Conference on Complex Systems 2023 in Brazil on 16 October 2023. This is a major event of the Complex System Society.

Advanced Lectures Series
The Disordered Systems group is hosting an Advanced Lectures series for PhD students, postdocs and all who want to attend and learn about advanced topics in the area of classical and quantum statistical mechanics of disordered and complex systems. These are lectures given by group members as well as visitors, in particular from the Distinguished Visitor series of the Maths Department. As part of this, Prof. Leonid Pastur delivered four very-well attended lectures on the subject of 'Quantum Entanglement in Disordered Systems.'

Journal of Statistical Mechanics Article Selected for Highlights Collection
Congratulations to Prof. Doyon (Department of Mathematics) and his collaborators, whose article 'Correlation functions and transport coefficients in generalised hydrodynamics' has been highlighted as part of the collection of noteworthy articles by the Scientific Directors from the articles published in JSTAT in recent months.

Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths
An article by Prof. Doyon and his student Dimitrios Ampelogiannis (Department of Mathematics) has been published in Annales Henri Poincaré, in a special issue dedicated to the memory of well-known mathematical physicist Krzysztof Gawedski. The article, entitled ' Long-Time Dynamics in Quantum Spin Lattices: Ergodicity and Hydrodynamic Projections at All Frequencies and Wavelengths' can be viewed via the below link.

Article published in Journal of Physics A
A recent article, 'Hydrodynamic gauge fixing and higher order hydrodynamic expansion' by Prof. Doyon (Department of Mathematics) and his collaborator has been published in the Journal of Physics.
.x937f4972.jpg?width=380&height=215&fit=crop&f=webp)
Reimer Kühn Appointed to Scientific Advisory Board
Congratulations to Reimer Kühn who has been appointed as a member of the Scientific Advisory Board for the Bielefeld Center for Interdisciplinary Research (ZiF) for a four-year tenure starting from October 2022.

'Physical Review E' Editorial Board Member Invitation
Congratulations to Izaak Neri, from the Disordered Systems Group in the Mathematics Department, who has been invited to be an editorial board member for the well-recognised journal, 'Physical Review E' (for the period of 2023-2025) of the American Physical Society.

Proceedings of Machine Learning Research Publication
In July 2022, the paper 'Fluctuations, Bias, Variance & Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension', co-authored by Gabriele Sicuro from the Disordered Systems Group at the Mathematics Department, was published in the prestigious international journal, Proceedings of Machine Learning Research. This was published in conjunction with the 39th International Conference on Machine Learning.

MECO47
Gabriele Sicuro and Pierpaolo Vivo from the Disordered Systems Group in the Mathematics Department, along with colleagues from UCL and IPhT Paris, organised the MECO47 in June 2022. MECO47 marked the 47th conference of the Middle European Cooperation in Statistical Physics (a famous international conference series in Statistical Physics). The hybrid event was held in Erice, Sicily from 12 June 2022 - 16 June 2022. There was a strong presence of the group at the conference, with Paola Ruggiero and Reimer Kuehn as speakers.
News
New framework uses games of chance to put 'price' on intangible assets
The new statistical model could have major implications for how data is bought and sold

Maths Professor at King's awarded top Institute of Physics prize for theoretical physics
Professor Benjamin Doyon received the 2022 John William Strutt, Lord Rayleigh Medal and Prize

King's women in maths: Tiziana Di Matteo
Tiziana Di Matteo interview

New graph-based visualisation interface for UK laws
New visualisation platform developed at King’s makes it easier to work with complex legal texts.

Events

Disordered Systems Days at King's College London
The Disordered Systems Group at King's College London are hosting a two-day event on the physics of disorder.
Please note: this event has passed.

Pointwise Ergodic Theory & Connections Conference
This is a conference about Pointwise Ergodic Theory, Discrete Harmonic Analysis and their connections, organised by Ben Krause, from the Department of...
Please note: this event has passed.
Seminars
The Disordered Systems group has a regular weekly informal seminar, usually held at 12:00 on Mondays.
The group also invites visitors to give seminars on Wednesday.
For more information, please email the seminar organiser, Matteo Tanzi on matteo.tanzi@kcl.ac.uk
The group also hosts an advanced lecture series, see https://dsadvancedlectures.weebly.com/ for information"