math-ph papers | Gist.Science

Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.

On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.

🔢 mathematics

Uniform analyticity of local observables in FK-percolation and analyticity of the Ising spontaneous magnetisation

This paper establishes the uniform analyticity of local observables in FK-percolation under mixing assumptions, a result that is leveraged to prove the analyticity of the Potts model's magnetisation (including the Ising case in all dimensions $d \geq 3$ within the supercritical regime) and susceptibility across the subcritical interval, as well as various connectivity probabilities.

Lucas D'Alimonte, Loïc Gassmann2026-04-21

🔢 mathematics

Efficient thermalization and universal quantum computing with quantum Gibbs samplers

This paper demonstrates that a specific family of efficiently implementable quasi-local dissipative evolutions can universally prepare high-temperature Gibbs states and their purifications in polynomial time, while also achieving computational universality equivalent to polynomial-time quantum computing in the low-temperature regime.

Cambyse Rouzé, Daniel Stilck França, Álvaro M. Alhambra2026-04-20

🔢 mathematics

Optimal Coherent Quantum Phase Estimation via Tapering

This paper introduces the tapered quantum phase estimation (tQPE) algorithm, which leverages classical signal processing window functions to achieve asymptotically optimal query complexity for coherent phase estimation without the high resource overhead of the standard coherent median technique, while also providing an efficiently preparable state that incurs at most a factor-of-two increase in error probability.

Dhrumil Patel, Shi Jie Samuel Tan, Yigit Subasi, Andrew T. Sornborger2026-04-20

🔢 mathematics

Network Renormalization

This review paper examines the challenges, key advances, and open problems in extending the renormalization group framework from traditional physical systems to the heterogeneous and geometrically complex realm of real-world networks.

Andrea Gabrielli, Diego Garlaschelli, Subodh P. Patil, M. Ángeles Serrano2026-04-20

🔢 mathematics

Global Gauge Symmetries and Spatial Asymptotic Boundary Conditions in Yang-Mills theory

This paper rigorously derives the physical gauge group of Yang-Mills theory as the quotient of boundary-preserving gauge transformations by Gauss law transformations by analyzing the structure of the instantaneous state space, and extends this analysis to demonstrate how boundary conditions and the resulting gauge group differ between the unbroken and broken phases of Yang-Mills-Higgs theory.

Silvester Borsboom, Hessel Posthuma2026-04-20

🔢 mathematics

Implicit representations of codimension-2 submanifolds and their prequantum structure

This paper establishes a prequantum bundle structure over the space of codimension-2 submanifolds by using complex-valued implicit representations, thereby offering a new geometric interpretation of the Marsden-Weinstein symplectic structure as the curvature of a connection form that measures the average volume swept by phase level set deformations.

Albert Chern, Sadashige Ishida2026-04-20

🔬 materials science

Perspective on Moreau-Yosida Regularization in Density-Functional Theory

This perspective paper reviews the application of Moreau-Yosida regularization in density-functional theory, highlighting its role in reformulating the Kohn-Sham approach, enabling density-potential inversion, and linking the theory to classical field theories, while outlining future development opportunities.

Markus Penz, Michael F. Herbst, Trygve Helgaker, Andre Laestadius2026-04-20

🔢 mathematics

Estimates to the weak solution of the electro-hydrodynamical boundary value problem for the unit cell of cation-exchange membrane

This paper analyzes a model of conducting fluid filtration through a porous layer composed of spherical cells with porous cores and liquid shells, deriving a priori estimates that prove the boundedness of velocity, pressure, electric potential, and ion flux densities while characterizing their dependence on the Debye radius.

Yulia Koroleva2026-04-20

🔬 mesoscale physics

Current-Induced Dynamics and Instability Pathways of Skyrmioniums in Chiral Magnets

This study combines micromagnetic simulations and analytical modeling to reveal how the internal structural imbalance of skyrmioniums drives a finite Hall effect and diverse current-induced instability pathways, while also characterizing the rich collective dynamics of skyrmionium-based meta-matter for potential applications in tunable nonequilibrium topological systems.

Kaito Nakamura, Yuka Kotorii, Andrey O. Leonov2026-04-20

🔢 mathematics

Characterizing all non-Hermitian degeneracies using algebraic approaches: Defectiveness and asymptotic behavior

This paper presents a rigorous algebraic framework to systematically characterize the asymptotic behavior and dispersion of all types of multi-block degeneracies in non-Hermitian systems under perturbations, offering a practical tool for analyzing complex experimental scenarios.

Sharareh Sayyad, Grigory A. Starkov2026-04-20

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