arXiv subjects

Parham Radpay

Publications and source records attributed to Parham Radpay.

8 recordsLinked to original sources

arXiv2026

Data Field Theory: Theory and Applications of the Functional Renormalization Group for Signal Detection

We review the renormalization group framework for signal detection in high-dimensional data, tailored to the regime where the signal may be of extensive rank and does not separate from the noise bulk as isolated spikes. The framework provides a conceptually simple criterion for distinguishing signal from noise within a quasi-continuous spectral region near a random-matrix universality class. This scenario lies beyond the reach of standard methods such as the Baik-Ben Arous-P\'ech\'e threshold, which requires eigenvalues to be cleanly separated from the bulk. The renormalization group approach, by contrast, directly tracks spectral deformations and consistently yields a lower limit of detection without relying on spike separation. We review results that identify the presence of a signal by testing the stability of the Gaussian fixed point of an effective field theory for the collective behaviour of the degrees of freedom in the spectral tail, where the signal resides. We also discuss how the scale dependence of the canonical dimension, induced by the signal, manifests as a dimensional phase transition.

physics.data-an↗

arXiv2026

Field Theory of Data: Anomaly Detection via the Functional Renormalization Group. The 2D Ising Model as a Benchmark

We establish a correspondence between anomaly detection in high-noise regimes and the renormalization group flow of non-equilibrium field theories. We provide a physical grounding for this framework by proving that the detection of phase transitions in interacting non-equilibrium systems maps to the study of an effective equilibrium field theory near its Gaussian fixed point, which we identify with the universal Marchenko-Pastur distribution. Applying the Functional Renormalization Group to the two-dimensional Model A, we demonstrate that the noise-to-signal ratio acts as a physical temperature, where the signal emerges as ordered domains within a thermalized background of fluctuations. Using the exact Onsager solution as a benchmark, we show that this approach identifies critical thresholds with an error below 4%, significantly outperforming standard information-theoretic metrics such as the Kullback-Leibler divergence. Our results provide a universal strategy for resolving structures in complex datasets near criticality, bridging the gap between statistical mechanics and statistical inference.

cond-mat.stat-mech↗

arXiv2025

On the injective norm of random fermionic states and skew-symmetric tensors

We study the injective norm of random skew-symmetric tensors and the associated fermionic quantum states, a natural measure of multipartite entanglement for systems of indistinguishable particles. Extending recent advances on random quantum states, we analyze both real and complex skew-symmetric Gaussian ensembles in two asymptotic regimes: fixed particle number with increasing one-particle Hilbert space dimension, and joint scaling with fixed filling fraction. Using the Kac--Rice formula on the Grassmann manifold, we derive high-probability upper bounds on the injective norm and establish sharp asymptotics in both regimes. Interestingly, a duality relation under particle--hole transformation is uncovered, revealing a symmetry of the injective norm under the action of the Hodge star operator. We complement our analytical results with numerical simulations for low fermion numbers, which match the predicted bounds.

math.PR↗

arXiv2025

Constructing the low-temperature phase diagram for the $2+p$-quantum spin glass using the nonperturbative renormalization group

In this paper, we use a nonperturbative renormalization group approach to construct the dynamical phase space of a quantum spin glass in the large $N$ limit. The disordered Hamiltonian is of ``$2 + p$" type, and we perform a coarse-graining procedure over the Wigner spectrum for the matrix-like disorder. The phase space reconstruction relies on phase transitions derived from the Luttinger-Ward functional, which accounts for interactions that are forbidden by perturbation theory. Various phases are identified, characterized by large correlations between replicas and/or the breaking of time translation symmetry.

cond-mat.dis-nn↗

arXiv2024

The quantum $p$-spin renormalization group in the large $N$ limit as a benchmark for functional renormalization group

To gain a deeper understanding of the glassy phase in $p$-spin quantum models, this paper examines the dynamics of the $N$-vector $\bm{x} \in \mathbb{R}^N$ through the framework of renormalization group theory. First, we focus on perturbation theory, which is more suitable than nonperturbative techniques due to the specific temporal non-locality of the model after disorder integration. We compute the one-loop $\beta$-function and explore the structure of its fixed points. Next, we develop the nonperturbative renormalization group approach based on the standard Wetterich-Morris formalism, using two approximation schemes to address the model's non-locality. We investigate the vertex expansion in the symmetric phase and assess the reliability of the approximations for the fixed-point solutions. Finally, we extend our analysis beyond the symmetric phase by using an expansion around the vacuum of the local potential. Our numerical investigations particularly focus on the cases $p = 2$ and $p=3$.

cond-mat.dis-nn↗

arXiv2024

Time-translation invariance symmetry breaking hidden by finite-scale singularities

In this paper, we consider a renormalization group perspective on the quantum dynamics of a particle moving in the Euclidean $\mathbb{R}^N$ space through the complex landscape provided by a disordered Hamiltonian of type $2+p$. We focus on the large $N$ limit, where the coarse-graining procedure is unconventional: it is based on the Wigner spectrum of the rank-2 disorder. The main consequence of this choice is that canonical dimensions depend on the scale, and the flow equations fail to become autonomous, preventing the existence of global fixed points. One of the main features of the underlying renormalization group flow is the existence of finite-scale singularities for initial conditions sufficiently close to the Gaussian region and for rank-$p$ disorder intensity large enough. Using the Luttinger-Ward formalism, we show that these finite-scale singularities hide (and should be resolved by) a phase transition that breaks time-translation invariance.

cond-mat.dis-nn↗

arXiv2024

Large time effective kinetics $\beta$-functions for quantum (2 + p)-spin glass II: Effective vertex expansion, local potential approximation and symmetries

This paper aims to study the functional renormalization group for quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$. By fixing the gauge symmetry in the construction of the FRG, that breaks the $O(N)$-symmetry and deriving the corresponding non-trivial Ward identity we can: In the first time coarse grain and focus on this study using a more attractive method such as the effective vertex expansion, and in the second time explore this model beyond the symmetry phase. We show finite scale singularities due to the disorder, interpreted as the signal in the perturbation theory. The unconventional renormalization group approach is based on coarse-graining over the eigenvalues of matrix-like disorder, viewed as an effective kinetic term, with an eigenvalue distribution following a deterministic law in the large $N$ limit. As an illustration, the case where $p=3$ is scrutinized.

cond-mat.dis-nn↗

arXiv2024

Large time effective kinetics $\beta$-functions for quantum (2+p)-spin glass

This paper examines the quantum $(2+p)$-spin dynamics of a $N$-vector $\textbf{x}\in \mathbb{R}^N$ through the lens of renormalization group (RG) theory. The RG is based on a coarse-graining over the eigenvalues of matrix-like disorder, viewed as an effective kinetic whose eigenvalue distribution undergoes a deterministic law in the large $N$ limit. We focus our investigation on perturbation theory and vertex expansion for effective average action, which proves more amenable than standard nonperturbative approaches due to the distinct non-local temporal and replicative structures that emerge in the effective interactions following disorder integration. Our work entails the formulation of rules to address these non-localities within the framework of perturbation theory, culminating in the derivation of one-loop $\beta$-functions. Our explicit calculations focus on the cases $p=3$, $p=\infty$, and additional analytic material is given in the appendix.

cond-mat.dis-nn↗