Random-field effects in spin models: Supersymmetry, criticality, and universality
Lead Research Organisation:
University of Essex
Department Name: Mathematical Sciences
Abstract
Statistical physics, one of the pillars of modern physics, describes how macroscopic experimental observations of a physical system (such as temperature and pressure) are related to microscopic variables, not seen with the naked eye. The beauty of the statistical physics approach lies in its ability to neatly describe phase transitions, such as ice melting, and other fundamental phenomena, including magnetism. However, the situation is more complicated: magnetic materials, which touch all technological aspects of our civilisation, contain impurities (disorder) that lead to unexplored properties and defy the standard framework. In fact, disorder is not only unavoidable in solid state materials and ubiquitous in realistic classical examples, but also quantum many-body systems. Disorder is responsible for a variety of interesting novel phenomena that do not have clean counterparts, such as the Anderson localisation, exotic quantum critical points, and glassy phases of matter, that appear solid on a short time scale, but continuously relax towards the liquid state. These phenomena are present in a wide range of condensed matter systems including polymers, metallic alloys, magnetic spin glasses, and many soft materials such as colloids, foams, emulsions or other complex fluids.
Understanding the effects of frustration and quenched disorder in condensed matter physics has immense technological consequences that reach up to the design and construction of quantum annealing devices used for future technologies of quantum computers. A vast amount of research has failed to reveal the physical mechanisms at play due to the rough energy landscape of these systems that disarms analytical and numerical approaches. Fortunately, years of consistent effort have enabled us to develop exceptionally versatile tools, including some extremely powerful numerical and theoretical approaches, that have unblocked the path towards a direct attack on the problem. Using this new toolbox of methods, the proposed project aims at clarifying the effects of random fields, one of the most common yet less understood types of disorder with many experimental analogues in physics, on a variety of spin models and unveiling their critical behaviour and universality principles. In addition, we also intend to clarify other ambiguous theoretical conjectures, like supersymmetry and dimensional reduction. We expect our results to pave the way for novel experiments and technological breakthroughs made possible by the development of an unambiguous interpretation of the underlying phenomena. As the concepts used for deciphering complexity in disordered systems apply to other fields involving emerging collective behaviour (e.g., financial markets, social networks), the progress achieved will underpin advancements in other scientific areas as well.
Understanding the effects of frustration and quenched disorder in condensed matter physics has immense technological consequences that reach up to the design and construction of quantum annealing devices used for future technologies of quantum computers. A vast amount of research has failed to reveal the physical mechanisms at play due to the rough energy landscape of these systems that disarms analytical and numerical approaches. Fortunately, years of consistent effort have enabled us to develop exceptionally versatile tools, including some extremely powerful numerical and theoretical approaches, that have unblocked the path towards a direct attack on the problem. Using this new toolbox of methods, the proposed project aims at clarifying the effects of random fields, one of the most common yet less understood types of disorder with many experimental analogues in physics, on a variety of spin models and unveiling their critical behaviour and universality principles. In addition, we also intend to clarify other ambiguous theoretical conjectures, like supersymmetry and dimensional reduction. We expect our results to pave the way for novel experiments and technological breakthroughs made possible by the development of an unambiguous interpretation of the underlying phenomena. As the concepts used for deciphering complexity in disordered systems apply to other fields involving emerging collective behaviour (e.g., financial markets, social networks), the progress achieved will underpin advancements in other scientific areas as well.
Organisations
- University of Essex (Lead Research Organisation)
- Gwangju Institute of Science and Technology (Collaboration)
- Dokuz Eylül University (Collaboration)
- Utrecht University (Collaboration)
- CIC nanoGUNE Consolidor (Collaboration)
- Sorbonne University (Paris IV & UPMC) (Project Partner)
- Complutense University of Madrid (Project Partner)
Publications

Moueddene L
(2024)
Critical and tricritical singularities from small-scale Monte Carlo simulations: the Blume-Capel model in two dimensions
in Journal of Statistical Mechanics: Theory and Experiment

Macêdo A
(2024)
Universal energy and magnetisation distributions in the Blume-Capel and Baxter-Wu models
in Journal of Statistical Mechanics: Theory and Experiment

Vatansever Z
(2024)
Monte Carlo study of the two-dimensional kinetic Ising model under a nonantisymmetric magnetic field
in Physical Review E

Moueddene L
(2024)
Critical and tricritical behavior of the d = 3 Blume-Capel model: Results from small-scale Monte Carlo simulations
in Physical Review E

Mataragkas D
(2025)
Tricriticality and finite-size scaling in the triangular Blume-Capel ferromagnet
in Physical Review Research

Vatansever E
(2024)
Dynamical critical behavior of the two-dimensional three-state Potts model.
in Physical review. E

Vatansever E
(2024)
Thermodynamic properties of disordered quantum spin ladders
in The European Physical Journal B


Vatansever E
(2024)
Dynamical critical behavior of the two-dimensional three-state Potts model
Description | Collaboration with CIC nanoGUNE BRTA, Spain |
Organisation | CIC nanoGUNE Consolidor |
Country | Spain |
Sector | Public |
PI Contribution | Numerical developments of efface t methods for the study of dynamical critical phenomena. |
Collaborator Contribution | Theoretical and experimental back up of dynamical critical phenomena. |
Impact | Monte Carlo study of the two-dimensional kinetic Ising model under a nonantisymmetric magnetic field Z. Demir Vatansever, E. Vatansever, A. Berger, A. Vasilopoulos, and N.G. Fytas Phys. Rev. E 110, 064155 (2024) |
Start Year | 2024 |
Description | Collaboration with the Department of Information and Computing Sciences, Utrecht University, the Netherlands |
Organisation | Utrecht University |
Country | Netherlands |
Sector | Academic/University |
PI Contribution | Investigation of the dynamical critical behaviour of the two-dimensional three-state Potts model with single spin-flip dynamics in equilibrium. |
Collaborator Contribution | Investigation of the dynamical critical behaviour of the two-dimensional three-state Potts model with single spin-flip dynamics in equilibrium. |
Impact | Dynamical critical behavior of the two-dimensional three-state Potts model E. Vatansever, G.T. Barkema, and N.G. Fytas Phys. Rev. E 110, 014135 (2024) |
Start Year | 2024 |
Description | Collaboration with the Department of Physics and Photon Science, Gwangju Institute of Science and Technology, South Korea |
Organisation | Gwangju Institute of Science and Technology |
Country | Korea, Republic of |
Sector | Academic/University |
PI Contribution | Development of novel simulation methods for studying tricriticality and finite-size scaling in spin models of statistical physics. |
Collaborator Contribution | Development of efficient numerical approaches of Monte Carlo type and investigation of universality principles of spin models in two dimensions. |
Impact | Tricriticality and finite-size scaling in the triangular Blume-Capel ferromagnet D. Mataragkas, A. Vasilopoulos, N.G. Fytas, and D.-H. Kim Phys. Rev. Research 7, 013214 (2025) This paper was also selected by the Editors of the American Physical Society as an Editor's Suggestion featured article. |
Start Year | 2024 |
Description | Collaboration with the Department of Physics, Dokuz Eylül University, Izmir-Turkey |
Organisation | Dokuz Eylül University |
Country | Turkey |
Sector | Academic/University |
PI Contribution | Development of numerical methods and investigation of dynamic phase transitions in kinetic spin models. Development of stochastic series expansion quantum Monte Carlo methods and investigation of thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders. |
Collaborator Contribution | Development of numerical methods and investigation of dynamic phase transitions in kinetic spin models. Development of stochastic series expansion quantum Monte Carlo methods and investigation of thermodynamic properties of spin-1/2 antiferromagnetic Heisenberg ladders. |
Impact | Monte Carlo study of the two-dimensional kinetic Ising model under a nonantisymmetric magnetic field Z. Demir Vatansever, E. Vatansever, A. Berger, A. Vasilopoulos, and N.G. Fytas Phys. Rev. E 110, 064155 (2024) Thermodynamic properties of disordered quantum spin ladders E. Vatansever, G.G. Grahovski, and N.G. Fytas Eur. Phys. J. B 97, 34 (2024) |
Start Year | 2024 |