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

Chiral Long-Range Order in three Euclidean Lattice Gross-Neveu Models

This paper rigorously proves the existence of long-range order in the chirally charged fermion-mass bilinear for a class of two-dimensional Euclidean lattice Gross-Neveu models with even flavor numbers by utilizing reflection positivity, chessboard estimates, and Peierls-type arguments to establish a non-perturbative connection between the lattice theory and large- $N$ mean-field predictions across various discretizations.

Simone Fabbri, Leonardo Goller2026-06-12

🔢 mathematics

Kubo-Martin-Schwinger conditions for non-Hermitian systems

This paper establishes that for diagonalizable non-Hermitian Hamiltonians with real spectra, the biorthogonal Gibbs functional satisfies the Kubo-Martin-Schwinger (KMS) condition if and only if the system is quasi-Hermitian, thereby providing a metric-free characterization of quasi-Hermiticity and proving that the resulting KMS states cannot be simply deduced from their Hermitian counterparts via similarity transformations.

Chen Lan, Luyao Ma, Hao Yang2026-06-12

🔢 mathematics

From 2D Yang-Mills to Calogero-Sutherland via a colored particle

This paper demonstrates that Yang-Mills theory coupled to a particle on a cylinder reduces to a finite-dimensional quantum system, yielding a Landau problem on a torus for the Abelian case and a one-dimensional Calogero-Sutherland-type many-body system for the non-Abelian SU(N) case.

Marcia Tenser, Amilcar R. Queiroz2026-06-12

🔢 mathematics

Rapid mixing for Gibbs measures in Riemannian manifolds

This paper establishes conditions involving manifold curvature, inverse temperature, and escaping directions from saddle points that guarantee polynomial mixing times for Langevin dynamics to Gibbs measures on Riemannian manifolds, thereby avoiding barren plateaus and spurious local minima through a novel relation between processes in the domain and their Riemannian submersion images.

Ángela Capel, Marco Castrillón-López, Sofyan Iblisdir, Angelo Lucia, Pablo Páez-Velasco, David Pérez-García2026-06-12

🔢 mathematics

Population dynamics of surface-mediated autocatalytic processes

This paper investigates the stochastic population dynamics of surface-mediated autocatalytic processes where particles diffuse and undergo competing replication or death events, providing a systematic theoretical analysis of the population's statistical properties across vanishing, steady-state, and exponential growth regimes supported by numerical solutions and Monte Carlo simulations.

Denis S. Grebenkov, Yilin Ye2026-06-12

🔢 mathematics

Quantum Logic Codes: Complete Transversal Logical Clifford Instruction Sets for High-Rate Stabilizer Quantum Error Correcting Codes

This paper introduces "Quantum Logic Codes," a family of high-rate stabilizer quantum error-correcting codes constructed from small base codes via tiling and concatenation that provably support a constant-depth, complete transversal logical Clifford instruction set architecture, including novel depth-one implementations of $\overline{S}$ and $\overline{CZ}$ gates.

Adam Holmes2026-06-12

🔢 mathematics

A ribbon ZX calculus for gauge theory

This paper generalizes the ZX calculus to two-dimensional Yang-Mills theory with a compact gauge group by leveraging a shared Hopf Frobenius algebraic structure, thereby establishing a foundation for applying this graphical formalism to low-dimensional gravity.

Gabriel Wong, Razin A. Shaikh, William Donnelly2026-06-12

🔢 mathematics

A Graphical Coaction for FRW Integrals from Partial/Relative Twisted (Co)homology

This paper introduces a graphical coaction framework for Friedmann-Robertson-Walker (FRW) integrals at all loop orders using intersection theory in twisted (co)homology to decompose cosmological observables into graph-based building blocks, thereby revealing the combinatorial structure of their governing differential equations and providing open-source tools for their computation.

Andrew J. McLeod, Andrzej Pokraka, Lecheng Ren2026-06-12

⚛️ high-energy theory

On the open TS/ST correspondence

This paper extends the topological string/spectral theory correspondence to the open string sector by constructing entire, off-shell eigenfunctions for the quantized mirror curve of local $\mathbb{F}_0$ from open topological string partition functions, and derives functional relations between the modified Mathieu and McCoy-Tracy-Wu operators in specific four-dimensional limits.

Matijn François, Alba Grassi2026-06-11

🔢 mathematics

The many faces of higher Hilbert spaces

This paper systematically unifies different notions of higher Hilbert spaces and their associated module categories by introducing $G$ -dagger categories and $G$ -Hermitian 2-vector spaces, where varying subgroups $G \leq O(2)$ recover distinct operator algebra structures like $\mathrm{C}^*$ , $\mathrm{W}^*$ , and $\mathrm{H}^*$ -algebras, while also proposing criteria for positivity and an inductive framework for arbitrary dimensions.

Giovanni Ferrer, Lukas Müller, David Penneys, Luuk Stehouwer2026-06-11

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