computational physics software developers

Abstract: Sampling from the ferromagnetic $q$-state Potts model is a fundamental problem in statistical physics and approximate counting. Although computationally hard in the worst case, sampling is expected to be efficient throughout the high-temperature uniqueness regime of the model using the natural single-site Glauber dynamics. We establish fast mixing bounds for every $q$, in the full high-temperature regimes in the two central graph families on $n$ vertices. (1) For every $Δ\ge 3$, the Potts Glauber dynamics mixes in $n\operatorname{polylog}(n)$ steps with high probability on a uniformly random $Δ$-regular graph for all $β<β_u(q,\mathbb T_Δ)$ where $β_u(q,\mathbb T_Δ)$ is the uniqueness threshold on the $Δ$-regular tree; (2) For every $d\ge 2$, the Potts Glauber dynamics has inverse spectral gap $n^{1+o(1)}$ on cubes or tori in $\mathbb Z^d$ for all $β<β_c(q,\mathbb Z^d)$ where $β_c(q,\mathbb Z^d)$ is the critical point on $\mathbb Z^d$. Both temperature thresholds are sharp as the Glauber dynamics slows down exponentially above them. These results overcome the challenge of bounding mixing times without access to correlation decay bounds in the presence of pinnings (i.e., without spectral independence or strong spatial mixing). For this purpose, our proof introduces a new dichotomy principle: throughout the high-temperature regime, any initial spin distribution is either such that its pinnings ensure good correlation decay, or Glauber dynamics escapes from that distribution quickly. We expect this kind of dichotomy to have further applications. As a demonstration, we also develop its analog for random-cluster dynamics and use it to prove that Swendsen-Wang dynamics on random $Δ$-regular graphs mixes in $O(\log n)$ time throughout uniqueness. The results in this paper were arrived at with the assistance of ChatGPT 5.6 and 6.

Abstract: Large-momentum effective theory (LaMET) provides a first-principles framework for computing the $x$ dependence of light-cone parton distributions from lattice QCD. Over the past decade, theoretical and numerical advances have established a mature multi-stage workflow for systematic calculation of parton physics, although its implementation still requires expert judgment and substantial repeated effort. We present lamet-agent, an open-source large language model (LLM) agent framework that organizes this workflow into an executable, reproducible, and inspectable analysis pipeline. The present release supports collinear quark distributions and implements correlator analysis, renormalization, Fourier transformation, perturbative matching, continuum, physical pion mass and infinite-momentum extrapolations, and automated result review. We validate it on four end-to-end analyses: pion parton distribution functions in the gauge-invariant and Coulomb-gauge formulations, and pion and kaon distribution amplitudes, obtaining results consistent with the published calculations. Extensions to transverse-momentum-dependent distributions, generalized transverse-momentum-dependent distributions, and gluonic distribution functions are planned for subsequent releases.

Abstract: Physics-informed neural networks and finite element methods provide two different paradigms for the numerical approximation of partial differential equations: the former are commonly trained by minimizing pointwise strong residuals, whereas the latter are naturally built from weak variational formulations and the finite-dimensional systems obtained after discretization. In this work, we introduce a common framework based on the discretization of functional Gauss--Newton problems by finite families of linear measurements. We show that, through an appropriate duality pairing, the linear measurements can be represented by test functions. The resulting Gauss--Newton system is then precisely a Petrov--Galerkin discretization of the linearized functional problem. This perspective recovers pointwise collocation and natural-gradient constructions as particular cases, while making the choice of test functions an explicit algorithmic design choice. We specialize this framework to elliptic problems, where it naturally leads to weak residual formulations and to a hybrid finite element--neural construction acting on complementary approximation spaces. Numerical experiments support the proposed framework and demonstrate the effectiveness of weak Gauss--Newton formulations and hybrid finite element--neural approximations.