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26333 results in Theoretical Physics and Mathematical Physics

Page 7 of 1317

  • PSP volume 180 issue 1 Cover and Front matter

  • Journal:
    Mathematical Proceedings of the Cambridge Philosophical Society / Volume 180 / Issue 1 / January 2026
    Published online by Cambridge University Press:
    19 December 2025, pp. f1-f2
    Print publication:
    January 2026
    • Article
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Phase Transitions in the Theory of Lattice Gases
  • Barry Simon
  • Published online:
    17 December 2025
    Print publication:
    13 November 2025
  • The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that. Topics covered include correlation inequalities, Lee-Yang theorems, the Peierls method, the Hohenberg-Mermin-Wagner method, infrared bounds, random cluster methods, random current methods and BKT transition. The final section outlines major open problems to inspire future work. This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

  • A construction of minimal coherent filling pairs

  • Part of
  • HONG CHANG, WILLIAM W. MENASCO
  • Journal:
    Mathematical Proceedings of the Cambridge Philosophical Society , First View
    Published online by Cambridge University Press:
    16 December 2025, pp. 1-22
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  • Let $S_g$ denote the genus g closed orientable surface. A coherent filling pair of simple closed curves, $(\alpha,\beta)$ in $S_g$, is a filling pair that has its geometric intersection number equal to the absolute value of its algebraic intersection number. A minimally intersecting filling pair, $(\alpha,\beta)$ in $S_g$, is one whose intersection number is the minimal among all filling pairs of $S_g$. In this paper, we give a simple geometric procedure for constructing minimally intersecting coherent filling pairs on $S_g, \ g \geq 3,$ from the starting point of a coherent filling pair of curves on a torus. Coherent filling pairs have a natural correspondence to square-tiled surfaces, or origamis, and we discuss the origami obtained from the construction.

  • How safe are the United Kingdom’s ports? A statistical analysis using accident data and AIS vessel movements

  • Iulia Manole, Arnab Majumdar, Alberto Garcia Sinobas
  • Journal:
    The Journal of Navigation , First View
    Published online by Cambridge University Press:
    11 December 2025, pp. 1-27
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  • Maritime safety faces growing challenges due to an expanding global fleet, tighter schedules, and increasingly complex stakeholder interactions. This study integrates multiple data sources to determine a more accurate representation of major marine accident causative factors in the United Kingdom. Logistic regression and data modelling are applied to Automatic Identification System data (2011–2017) and reported accidents from the Marine Accident Investigation Branch (2013–2019). Results show that larger vessels, daytime transits, service ships, winter conditions, and confined high-density areas such as ports impact accident likelihood. Interviews validate the data and emphasize the influence of port geometry and channel complexity. Among major UK ports, London, Plymouth and Milford Haven exhibit the highest accident-to-traffic densities. While maritime regulations and safety management systems in ports and vessels are seen as adequate by industry professionals, human factors require the greatest attention to improve maritime safety.

  • The rational (non-)formality of the non-3-equal manifolds

  • Part of
  • JESÚS GONZÁLEZ, JOSÉ LUIS LEÓN–MEDINA
  • Journal:
    Mathematical Proceedings of the Cambridge Philosophical Society , First View
    Published online by Cambridge University Press:
    08 December 2025, pp. 1-17
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  • Let $M^{({k})}_{d}(n)$ be the manifold of n-tuples $(x_1,\ldots,x_n)\in(\mathbb{R}^d)^n$ having non-k-equal coordinates. We show that, for $d\geq2$, $M^{({3})}_{d}(n)$ is rationally formal if and only if $n\leq6$. This stands in sharp contrast with the fact that all classical configuration spaces $M^{({2})}_d(n)=\text{Conf}(\mathbb{R}^d,n)$ are rationally formal, just as are all complements of arrangements of arbitrary complex subspaces with geometric lattice of intersections. The rational non-formality of $M^{({3})}_{d}(n)$ for $n \gt 6$ is established via detection of non-trivial triple Massey products, which are assessed geometrically through Poincaré duality.

  • WiFi-RTT indoor positioning using Particle, Genetic and Grid filters with RSSI-based outlier detection

  • Khalil Jibran Raja, Paul D. Groves
  • Journal:
    The Journal of Navigation , First View
    Published online by Cambridge University Press:
    04 December 2025, pp. 1-19
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  • The paper explores the accuracy of WiFi-Round Trip Timing (RTT) positioning in indoor environments. Filtering techniques are applied to WiFi-RTT positioning in indoor environments, enhanced by Residual Signal Strength Indicator (RSSI)-based outlier detection. A Genetic and Grid filter are compared with a Particle filter and single-epoch least-squares across a range of test scenarios. In static scenarios, 67% of trials had sub-metre accuracy and 90.5% had a root mean square error (RMSE) below 2 m. In Non-Line-of-Sight (NLOS) conditions, 38% of trials had sub-metre accuracy, whereas for environments with full Line-of-Sight (LOS) conditions, 95.2% of trials had sub-metre accuracy. In scenarios with motion, 22.2% of trials had sub-metre accuracy. RSSI-based outlier detection in NLOS conditions, provided an average improvement of 41.3% over no outlier detection across all algorithms in the static and 14% in the dynamic tests. The Genetic filter achieved a mean improvement of 49.2% in the static and 47% in the dynamic tests compared with least squares.

  • Wayfinding behaviours in natural environments

  • Ole Edward Wattne, Frode Volden
  • Journal:
    The Journal of Navigation , First View
    Published online by Cambridge University Press:
    25 November 2025, pp. 1-15
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  • Adapting Barker’s ((2019). The Journal of Navigation, 72(3), 539–554) taxonomy of wayfinding behaviours – originally developed for man-made environments, paper and screen – we examined which behaviours are also found in the outdoors. In the analysis of the collected data from a questionnaire (n=401), we find that participants employ every category in Barker’s framework of social, semantic and spatial behaviours. Our respondents report the use of digital maps on a mobile phone as the most common behaviour, with following directional signs as the second most used. Furthermore, social wayfinding behaviours figure prominently and the participants express preferences for various information sources. We demonstrate similarities of behaviours across the different types of environments and we confirm the applicability of Barker’s taxonomy of wayfinding behaviours also in nature. Our study generates knowledge that potentially can make navigation simpler and more efficient through wayfinding design, and lead to heightened feeling of safety in the outdoors. Wayfinding behaviour studies, like this one, can serve as a bridge between human psychology and practical design.

Causal Fermion Systems
  • An Introduction to Fundamental Structures, Methods and Applications
  • Felix Finster, Sebastian Kindermann, Jan‐Hendrik Treude
  • Published online:
    15 November 2025
    Print publication:
    23 October 2025
  • The theory of causal fermion systems represents a novel approach to fundamental physics and is a promising candidate for a unified physical theory. This book offers a comprehensive overview of the theory, structured in four parts: the first lays the necessary mathematical and physical foundations; the second offers an introduction to the theory and the causal action principle; the third describes the mathematical tools for analyzing causal fermion systems; and the fourth gives an outlook on the key physical applications. With relevance across mathematical and theoretical physics, the book is aimed at graduate students and researchers interested in novel approaches to the structure of spacetime and alternative perspectives to the more established quantum field theories. It can be used for advanced courses in the subject or as a reference for research and self-guided study. Exercises are included at the end of each chapter to build and develop key concepts.

  • Local central limit theorem for triangle counts in sparse random graphs

  • Part of
  • PEDRO ARAÚJO, LETÍCIA MATTOS
  • Journal:
    Mathematical Proceedings of the Cambridge Philosophical Society / Volume 180 / Issue 2 / March 2026
    Published online by Cambridge University Press:
    14 November 2025, pp. 459-475
    Print publication:
    March 2026

  • Let $X_H$ be the number of copies of a fixed graph H in G(n,p). In 2016, Gilmer and Kopparty conjectured that a local central limit theorem should hold for $X_H$ as long as H is connected, $p\gg n^{-1/m(H)}$ and $n^2(1-p)\gg 1$, where m(H) denotes the m-density of H. Recently, Sah and Sawhney showed that the Gilmer–Kopparty conjecture holds for constant p. In this paper, we show that the Gilmer–Kopparty conjecture holds for triangle counts in the sparse range. More precisely, if $p \in (4n^{-1/2}, 1/2)$, then

    \[ {} {} {}\sup_{x\in \mathcal{L}}\left| \dfrac{1}{\sqrt{2\pi}}e^{-x^2/2}-\sigma\cdot \mathbb{P}(X^* = x)\right|=n^{-1/2+o(1)}p^{1/2}, {} {}\]
    where $\sigma^2 = \mathbb{V}\text{ar}(X_{K_3})$, $X^{*}=(X_{K_3}-\mathbb{E}(X_{K_3}))/\sigma$ and $\mathcal{L}$ is the support of $X^*$. By combining our result with the results of Röllin–Ross and Gilmer–Kopparty, this establishes the Gilmer–Kopparty conjecture for triangle counts for $n^{-1}\ll p \lt c$, for any constant $c\in (0,1)$. Our quantitative result is enough to prove that the triangle counts converge to an associated normal distribution also in the $\ell_1$-distance. This is the first local central limit theorem for subgraph counts above the so-called $m_2$-density threshold.

  • 2 - Correlation Inequalities

  • Barry Simon, California Institute of Technology
  • Book:
    Phase Transitions in the Theory of Lattice Gases
    Published online:
    17 December 2025
    Print publication:
    13 November 2025, pp 39-205

  • Summary

    The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that.

    Topics covered include correlation inequalities, Lee–Yang theorems, the Peierls method, the Hohenberg–Mermin–Wagner method, infrared bounds, random cluster methods, random current methods, and BKT transition. The final section outlines major open problems to inspire future work.

    This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

  • 4 - Peierls Argument

  • Barry Simon, California Institute of Technology
  • Book:
    Phase Transitions in the Theory of Lattice Gases
    Published online:
    17 December 2025
    Print publication:
    13 November 2025, pp 283-345

  • Summary

    The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that.

    Topics covered include correlation inequalities, Lee–Yang theorems, the Peierls method, the Hohenberg–Mermin–Wagner method, infrared bounds, random cluster methods, random current methods, and BKT transition. The final section outlines major open problems to inspire future work.

    This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

  • 7 - Stochastic Geometric Representations

  • Barry Simon, California Institute of Technology
  • Book:
    Phase Transitions in the Theory of Lattice Gases
    Published online:
    17 December 2025
    Print publication:
    13 November 2025, pp 427-507

  • Summary

    The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that.

    Topics covered include correlation inequalities, Lee–Yang theorems, the Peierls method, the Hohenberg–Mermin–Wagner method, infrared bounds, random cluster methods, random current methods, and BKT transition. The final section outlines major open problems to inspire future work.

    This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

  • 9 - Final Thoughts

  • Barry Simon, California Institute of Technology
  • Book:
    Phase Transitions in the Theory of Lattice Gases
    Published online:
    17 December 2025
    Print publication:
    13 November 2025, pp 557-570

  • Summary

    The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that.

    Topics covered include correlation inequalities, Lee–Yang theorems, the Peierls method, the Hohenberg–Mermin–Wagner method, infrared bounds, random cluster methods, random current methods, and BKT transition. The final section outlines major open problems to inspire future work.

    This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

  • 1 - A Framework for Lattice Gases

  • Barry Simon, California Institute of Technology
  • Book:
    Phase Transitions in the Theory of Lattice Gases
    Published online:
    17 December 2025
    Print publication:
    13 November 2025, pp 1-38
    • Chapter
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  • Summary

    The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that.

    Topics covered include correlation inequalities, Lee–Yang theorems, the Peierls method, the Hohenberg–Mermin–Wagner method, infrared bounds, random cluster methods, random current methods, and BKT transition. The final section outlines major open problems to inspire future work.

    This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

  • 3 - The Lee–Yang Theorem

  • Barry Simon, California Institute of Technology
  • Book:
    Phase Transitions in the Theory of Lattice Gases
    Published online:
    17 December 2025
    Print publication:
    13 November 2025, pp 206-282

  • Summary

    The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that.

    Topics covered include correlation inequalities, Lee–Yang theorems, the Peierls method, the Hohenberg–Mermin–Wagner method, infrared bounds, random cluster methods, random current methods, and BKT transition. The final section outlines major open problems to inspire future work.

    This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

Page 7 of 1317