38 research outputs found
The New Science of Long Data
No full textAlessandro Codello’s contribution introduces “Long Data” as a novel approach to unlocking the cultural heritage within historical archives. This concept contrasts with Big Data by focusing on the deep historical context found in meticulously preserved archives, revealing insights into cultural heritage. Utilizing new Artificial Intelligence technologies in harmony with traditional archival methods, Long Data aims to analyze, transcribe, and model historical data on an unprecedented scale. This approach promises a more comprehensive understanding of history, enhancing studies on societal and cultural evolution. A key example of Long Data’s application is the Venice State Archive (ASVe), which holds over a millennium’s worth of documents. The initiative seeks multidisciplinary collaboration to make accessible this vast archive, thereby safeguarding its cultural heritage and preparing the ground for a revolution in historical research
Criticality of spin systems with weak long-range interactions
No full textThe study of critical properties of systems with long-range interactions has attracted, in recent decades, a continuing interest and motivated the development of several analytical and numerical techniques, in particular in connection with spin models. From the point of view of the investigation of their criticality, a special role is played by systems in which the interactions are long-range enough that their universality class is different from the short-range case and, nevertheless, they maintain the extensivity of thermodynamical quantities. Such interactions are often called weak long-range. In this paper we focus on the study of the critical behaviour of spin systems with weak-long range couplings using functional renormalization group, and we review their remarkable properties. For the sake of clarity and self-consistency, we start from classical spin models and we then move to quantum spin systems
On the covariant formalism of the effective field theory of gravity and its cosmological implications
Get PDFFollowing our previous work wherein the leading order effective action was computed in the covariant effective field theory of gravity, here we specialize the effective action to the FRW spacetime and obtain the effective Friedmann equations. In particular, we focus our attention on studying the cosmological implications of the non-local terms when each of them is combined with the Einstein-Hilbert action. We obtain both analytical and iterative solutions to the effective background equations in all the cases and also briefly comment on the consistency between the iterative and numerical solutions whenever possible. We find that among all the non-local terms, the imprints induced by R1/2R are very significant. Interpreting these corrections as an effective dark energy component characterized by an equation of state parameter, we find that the R1/2R correction can indeed lead to an accelerated expansion of the universe at the present epoch even in the absence of a cosmological constant. We briefly discuss some phenomenological consequences of our results.</p
Fixed points of nonlinear sigma models in d>2
No full textAbstractUsing Wilsonian methods, we study the renormalization group flow of the nonlinear sigma model in any dimension d, restricting our attention to terms with two derivatives. At one loop we always find a Ricci-type flow. When symmetries completely fix the internal metric, we compute the beta function of the single remaining coupling, without any further approximation. For d>2 and positive curvature, there is a nontrivial fixed point, which could be used to define an ultraviolet limit, in spite of the perturbative nonrenormalizability of the theory. Potential applications are briefly mentioned
On the covariant formalism of the effective field theory of gravity and leading order corrections
No full textWe construct the covariant effective field theory of gravity as an expansion in inverse powers of the Planck mass, identifying the leading and next-to-leading quantum corrections. We determine the form of the effective action for the cases of pure gravity with cosmological constant as well as gravity coupled to matter. By means of heat kernel methods we renormalize and compute the leading quantum corrections to quadratic order in a curvature expansion. The final effective action in our covariant formalism is generally non-local and can be readily used to understand the phenomenology on different spacetimes. In particular, we point out that on curved backgrounds the observable leading quantum gravitational effects are less suppressed than on Minkowski spacetime.</p
On the non-local heat kernel expansion
Get PDFWe propose a novel derivation of the non-local heat kernel expansion, first studied by Barvinsky, Vilkovisky, and Avramidi, based on simple diagrammatic equations satisfied by the heat kernel. For Laplace-type differential operators, we obtain the explicit form of the non-local heat kernel form factors to second order in the curvatures. Our method can be generalized easily to the derivation of the non-local heat kernel expansion of a wide class of differential operators. © 2013 American Institute of Physics
Structural aspects of FRG in quantum tunnelling computations
Get PDFWe probe both the unidimensional quartic harmonic oscillator and the double
well potential through a numerical analysis of the Functional Renormalization
Group flow equations truncated at first order in the derivative expansion. The
two partial differential equations for the potential V_k(varphi) and the wave
function renormalization Z_k(varphi), as obtained in different schemes and with
distinct regulators, are studied down to k=0, and the energy gap between lowest
and first excited state is computed, in order to test the reliability of the
approach in a strongly non-perturbative regime. Our findings point out at least
three ranges of the quartic coupling lambda, one with higher lambda where the
lowest order approximation is already accurate, the intermediate one where the
inclusion of the first correction produces a good agreement with the exact
results and, finally, the one with smallest lambda where presumably the higher
order correction of the flow is needed. Some details of the specifics of the
infrared regulator are also discussed.Comment: 19 pages, 7 figure
