Searcharxiv⌕ Search

arXiv subjects

Alessandro Giuliani

Publications and source records attributed to Alessandro Giuliani.

At least 19 recordsLinked to original sources
arXiv2026

The conductivity matrix at the topological phase transition

For a general class of two-dimensional non-interacting semi-metallic electron systems on a lattice, we derive an explicit formula for the whole conductivity matrix, by using Euclidean many-body formalism. The semi-metallic phase takes place whenever two Bloch bands touch at the Fermi energy with conical intersections and generally occurs at the transition between distinct integer quantum Hall phases. Unlike the longitudinal conductivity (which depends solely on the shape of the cones at the Fermi level), the transverse conductivity is remarkably determined both by the conical structures of the bands and by the nature of the two nearby topological phases. Generically, in the semi-metallic state, neither the longitudinal nor the transverse conductivities are quantized in integer multiples of a universal conductivity quantum; however, universality of the conductivity matrix is restored under the assumption of emergent rotational symmetry of the linearized Hamiltonian at the Fermi points. Using our formula, we compute the conductivity matrix for several physically relevant models of quantum Hall fluids at the topological phase transition, exhibiting cases where the transverse conductivity is quantized in half-integer multiples of $e^2/h$ and cases where it depends continuously on an external strain parameter, thus shedding light on its universality or non-universality features.

math-ph↗
arXiv2025

Universality of the topological phase transition in the interacting Haldane model

The Haldane model is a standard tight-binding model describing electrons hopping on a hexagonal lattice subject to a transverse, dipolar magnetic field. We consider its interacting version for values of the interaction strength that are small compared to the bandwidth. We study the critical case at the transition between the trivial and the `topological' insulating phases, and we rigorously establish that the transverse conductivity on the dressed critical line is quantized at a half-integer multiple of $e^2/h$: this is the average of the integer values of the Hall conductivity in the insulating phases on either side of the dressed critical line. Together with previous results, this fully characterizes the nature of the phase transition between different Hall plateaus and proves its universality with respect to many-body interactions. The proof is based on a combination of constructive renormalization group methods and exact lattice Ward identities.

cond-mat.str-el↗
arXiv2024

LIMBA: An Open-Source Framework for the Preservation and Valorization of Low-Resource Languages using Generative Models

Minority languages are vital to preserving cultural heritage, yet they face growing risks of extinction due to limited digital resources and the dominance of artificial intelligence models trained on high-resource languages. This white paper proposes a framework to generate linguistic tools for low-resource languages, focusing on data creation to support the development of language models that can aid in preservation efforts. Sardinian, an endangered language, serves as the case study to demonstrate the framework's effectiveness. By addressing the data scarcity that hinders intelligent applications for such languages, we contribute to promoting linguistic diversity and support ongoing efforts in language standardization and revitalization through modern technologies.

cs.CL↗
arXiv2024

The scaling limit of boundary spin correlations in non-integrable Ising models

We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip symmetry, and we study its critical theory in the half-plane. We prove that the leading order long-distance behavior of the correlation functions for spins on the boundary is the same as for the nearest-neighbor model, up to an analytic multiplicative renormalization constant. In particular, the scaling limit is the Pfaffian of an explicit matrix. The proof is based on an exact representation of the generating function of correlations in terms of a Grassmann integral and on a multiscale analysis thereof, generalizing previous results to include observables located on the boundary.

math-ph↗
arXiv2024

Non-trivial fixed point of a $\psi^4_d$ fermionic theory, II. Anomalous exponent and scaling operators

We consider the Renormalization Group (RG) fixed-point theory associated with a fermionic $\psi^4_d$ model in $d=1,2,3$ with fractional kinetic term, whose scaling dimension is fixed so that the quartic interaction is weakly relevant in the RG sense. The model is defined in terms of a Grassmann functional integral with interaction $V^*$, solving a fixed-point RG equation in the presence of external fields, and a fixed ultraviolet cutoff. We define and construct the field and density scale-invariant response functions, and prove that the critical exponent of the former is the naive one, while that of the latter is anomalous and analytic. We construct the corresponding (almost-)scaling operators, whose two point correlations are scale-invariant up to a remainder term, which decays like a stretched exponential at distances larger than the inverse of the ultraviolet cutoff. Our proof is based on constructive RG methods and, specifically, on a convergent tree expansion for the generating function of correlations, which generalizes the approach developed by three of the authors in a previous publication [A. Giuliani, V. Mastropietro, S. Rychkov, JHEP 01 (2021) 026].

math-ph↗
arXiv2023

Iterative Zero-Shot LLM Prompting for Knowledge Graph Construction

In the current digitalization era, capturing and effectively representing knowledge is crucial in most real-world scenarios. In this context, knowledge graphs represent a potent tool for retrieving and organizing a vast amount of information in a properly interconnected and interpretable structure. However, their generation is still challenging and often requires considerable human effort and domain expertise, hampering the scalability and flexibility across different application fields. This paper proposes an innovative knowledge graph generation approach that leverages the potential of the latest generative large language models, such as GPT-3.5, that can address all the main critical issues in knowledge graph building. The approach is conveyed in a pipeline that comprises novel iterative zero-shot and external knowledge-agnostic strategies in the main stages of the generation process. Our unique manifold approach may encompass significant benefits to the scientific community. In particular, the main contribution can be summarized by: (i) an innovative strategy for iteratively prompting large language models to extract relevant components of the final graph; (ii) a zero-shot strategy for each prompt, meaning that there is no need for providing examples for "guiding" the prompt result; (iii) a scalable solution, as the adoption of LLMs avoids the need for any external resources or human expertise. To assess the effectiveness of our proposed model, we performed experiments on a dataset that covered a specific domain. We claim that our proposal is a suitable solution for scalable and versatile knowledge graph construction and may be applied to different and novel contexts.

cs.CL↗
arXiv2023

Low temperature asymptotic expansion for classical $O(N)$ vector models

We consider classical $O(N)$ vector models in dimension three and higher and investigate the nature of the low-temperature expansions for their multipoint spin correlations. We prove that such expansions define asymptotic series, and derive explicit estimates on the error terms associated with their finite order truncations. The result applies, in particular, to the spontaneous magnetization of the 3D Heisenberg model. The proof combines a priori bounds on the moments of the local spin observables, following from reflection positivity and the infrared bound, with an integration-by-parts method applied systematically to a suitable integral representation of the correlation functions. Our method generalizes an approach, proposed originally by Bricmont and collaborators [6] in the context of the rotator model, to the case of non-abelian symmetry and non-gradient observables.

math-ph↗
arXiv2022

Upper bound for the ground state energy of a dilute Bose gas of hard spheres

We consider a gas of bosons interacting through a hard-sphere potential with radius $\frak{a}$ in the thermodynamic limit. We derive a simple upper bound for the ground state energy per particle at low density. Our bound captures the leading term $4\pi \rho \frak{a}$ and shows that corrections are smaller than $C \rho \frak{a} (\rho \frak{a}^3)^{1/2}$, for a sufficiently large constant $C > 0$. In combination with a known lower bound, our result implies that the first sub-leading term to the ground state energy is, in fact, of the order $\rho \frak{a} (\rho \frak{a}^3)^{1/2}$, in agreement with the Lee-Huang-Yang prediction.

math-ph↗
arXiv2022

Reconstruction of the temporal correlation network of all-cause mortality fluctuation across Italian regions: the importance of temperature and among-nodes flux

All-cause mortality is a very coarse grain, albeit very reliable, index to check the health implications of lifestyle determinants, systemic threats and socio-demographic factors. In this work we adopt a statistical-mechanics approach to the analysis of temporal fluctuations of all-cause mortality, focusing on the correlation structure of this index across different regions of Italy. The correlation network among the 20 Italian regions was reconstructed using temperature oscillations and travellers' flux (as a function of distance and region's attractiveness, based on GDP), allowing for a separation between infective and non-infective death causes. The proposed approach allows monitoring of emerging systemic threats in terms of anomalies of correlation network structure.

q-bio.PE↗
arXiv2022

Periodic striped states in Ising models with dipolar interactions

We review the problem of determining the ground states of 2D Ising models with nearest neighbor ferromagnetic and dipolar interactions, and prove a new result supporting the conjecture that, if the nearest neighbor coupling $J$ is sufficiently large, the ground states are periodic and `striped'. More precisely, we prove a restricted version of the conjecture, by constructing the minimizers within the variational class of states whose domain walls are arbitrary collections of horizontal and/or vertical straight lines.

math-ph↗
arXiv2022

Weakly non-planar dimers

We study a model of fully-packed dimer configurations (or perfect matchings) on a bipartite periodic graph that is two-dimensional but not planar. The graph is obtained from $\mathbb Z^2$ via the addition of an extensive number of extra edges that break planarity (but not bipartiteness). We prove that, if the weight $\lambda$ of the non-planar edges is small enough, a suitably defined height function scales on large distances to the Gaussian Free Field with a $\lambda$-dependent amplitude, that coincides with the anomalous exponent of dimer-dimer correlations. Because of non-planarity, Kasteleyn's theory does not apply: the model is not integrable. Rather, we map the model to a system of interacting lattice fermions in the Luttinger universality class, which we then analyze via fermionic Renormalization Group methods.

math.PR↗
arXiv2022

Design and Development of PCN-Miner: A tool for the Analysis of Protein Contact Networks

Protein Contact Network (PCN) is a powerful tool for analysing the structure and function of proteins. In particular, PCN has been used for disclosing the molecular features of allosteric regulation through PCN clustering. Such analysis is relevant in many applications, such as the recent study of SARS-CoV-2 Spike Protein. Despite its relevance, methods for the analysis of PCN are spread into a set of different libraries and tools. Therefore, the introduction of a tool that incorporates all the function may help researchers. We present PCN-Miner a software tool implemented in the Python programming language able to import protein in the Protein Data Bank format and generate the corresponding protein contact network. Then it offers a set of algorithms for the analysis of PCS that cover a large set of applications: from clustering to embedding and subsequent analysis. Software is available at \url{https://github.com/hguzzi/ProteinContactNetworks}

q-bio.QM↗
arXiv2021

Long range order in atomistic models for solids

The emergence of long-range order at low temperatures in atomistic systems with continuous symmetry is a fundamental, yet poorly understood phenomenon in Physics. To address this challenge we study a discrete microscopic model for an elastic crystal with dislocations in three dimensions, previously introduced by Ariza and Ortiz. The model is rich enough to support some realistic features of three-dimensional dislocation theory, most notably grains and the Read-Shockley law for grain boundaries, which we rigorously derive in a simple, explicit, geometry. We analyze the model at positive temperatures, in terms of a Gibbs distribution with energy function given by the Ariza-Ortiz Hamiltonian plus a contribution from the dislocation cores. Our main result is that the model exhibits long range positional order at low temperatures. The proof is based on the tools of discrete exterior calculus, together with cluster expansion techniques.

math.AP↗
arXiv2021

Scaling limits and universality of Ising and dimer models

After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of lattice critical models, including a quantitative characterization of the limiting distribution and the robustness of the limit under perturbations of the microscopic Hamiltonian. Specifically, I focus on two classes of non-exactly-solvable two-dimensional systems: non-planar Ising models and interacting dimers. In both settings, I describe the conjectures on the expected structure of the scaling limit, review the progress towards their proof, and state some of the recent results on the universality of the limit, which I contributed to. Finally, I outline the ideas and methods involved in the proofs, describe some of the perspectives opened by these results, and propose several open problems.

math-ph↗
arXiv2021

Non-integrable Ising models in cylindrical geometry: Grassmann representation and infinite volume limit

In this paper, meant as a companion to arXiv:2006.04458, we consider a class of non-integrable $2D$ Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a detailed derivation of the Grassmann representation of the model, including a self-contained presentation of the exact solution of the nearest neighbor model in the cylinder. Moreover, we prove precise asymptotic estimates of the fermionic Green's function in the cylinder, required for the multiscale analysis of the model. We also review the multiscale construction of the effective potentials in the infinite volume limit, in a form suitable for the generalization to finite cylinders. Compared to previous works, we introduce a few important simplifications in the localization procedure and in the iterative bounds on the kernels of the effective potentials, which are crucial for the adaptation of the construction to domains with boundaries.

math-ph↗
arXiv2021

FootApp: an AI-Powered System for Football Match Annotation

In the last years, scientific and industrial research has experienced a growing interest in acquiring large annotated data sets to train artificial intelligence algorithms for tackling problems in different domains. In this context, we have observed that even the market for football data has substantially grown. The analysis of football matches relies on the annotation of both individual players' and team actions, as well as the athletic performance of players. Consequently, annotating football events at a fine-grained level is a very expensive and error-prone task. Most existing semi-automatic tools for football match annotation rely on cameras and computer vision. However, those tools fall short in capturing team dynamics, and in extracting data of players who are not visible in the camera frame. To address these issues, in this manuscript we present FootApp, an AI-based system for football match annotation. First, our system relies on an advanced and mixed user interface that exploits both vocal and touch interaction. Second, the motor performance of players is captured and processed by applying machine learning algorithms to data collected from inertial sensors worn by players. Artificial intelligence techniques are then used to check the consistency of generated labels, including those regarding the physical activity of players, to automatically recognize annotation errors. Notably, we implemented a full prototype of the proposed system, performing experiments to show its effectiveness in a real-world adoption scenario.

cs.HC↗
arXiv2021

Conformal invariance and Renormalization Group

Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a quantum critical point. Conformal invariance is expected to be a feature of the fixed point theory obtained from a microscopic model at criticality, under appropriate averaging and rescaling operations: the action of the Wilsonian Renormalization Group (RG). Unfortunately, an explicit connection between critical microscopic models and their conformally invariant scaling limit is still lacking in general. Nevertheless, the last decades witnessed significant progress on this topic, both from the mathematical and physics sides, where several new tools have been introduced and their ranges of applications have constantly and significantly increased: I refer here, e.g., to discrete holomorphicity, SLE, the use of lattice Ward Identities in constructive RG, the conformal bootstrap program and its recent applications to 3D CFT. In an effort to make further progress on these problems, the one-day workshop "Emergent CFTs in statistical mechanics" was organized: the goal was to bring together probabilists, mathematical physicists and theoretical physicists, working on various aspects of critical statistical mechanics systems with complementary tools, both at the discrete and the continuum level, in the hope of creating new connections between the different approaches. This paper is based on an introductory talk given at the workshop: after a summary of the main topics discussed in the meeting, I illustrate the approach to the problem based on constructive RG methods, by reviewing recent results on the existence and the explicit characterization of the scaling limit of critical 2D Ising models with finite range interactions in cylindrical geometry.

math-ph↗