arXiv subjects

Alicia Castro

Publications and source records attributed to Alicia Castro.

11 recordsLinked to original sources

arXiv2026

Towards a quantitative characterization of gravitational universality classes for order-4 random tensor models

Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random matrices. This limit corresponds to a fixed point of a pregeometric Renormalization Group flow in which the tensor size $N$ serves as the Renormalization Group scale. We search for corresponding fixed points in order-4 random tensor models associated to dynamical triangulations in 4 dimensions. In a $O(N)^{\otimes 4}$ symmetric setting, we discuss the resulting phase portrait as a function of the regulator parameters. We optimize our results, identifying parameter values for which the results are minimally sensitive to parameter changes. We find three fixed-point candidates: only one of them is real across the entire parameter range, but only has two relevant directions. This should be contrasted with the university class of the Reuter fixed point in continuum quantum gravity, very likely characterized by three relevant directions. We conclude that simple combinatorial models of Euclidean triangulations and the Reuter fixed point most likely lie in different universality classes.

gr-qc↗

arXiv2025

An equivalence in random matrix and tensor models via a dually weighted intermediate field representation

We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that the partition functions of certain self-adjoint models and their complex counterparts are different integral representations of the exact same function. A special case of these equivalences takes a form of newly found dually weighted intermediate field representations, which generalize the standard intermediate field representation. We also find indications of an equivalence between real tensor models and self-transpose tensor models.

math-ph↗

arXiv2025

Numerical estimation of the Hausdorff dimension of D-random feuilletages

We implement numerical techniques to simulate D-random feuilletages, candidates for higher-dimensional random geometries introduced in L. Lionni and J.-F. Marckert, Math. Phys. Anal. Geom. 24 (2021) 39. Using finite-size scaling techniques, our approach allows to give a numerical estimation of the Hausdorff dimension $d_H$ of these feuilletages. The results obtained are compatible with the formal result known for the Brownian map, which corresponds to the D=2 random feuilletage. For the D=3 case, our numerical study finds a good agreement with the conjectured value $d_H=8$.

math-ph↗

arXiv2025

The massive BMS character in 3D quantum gravity

We derive the one-loop partition function for three-dimensional quantum gravity in a finite-radius thermal twisted flat space with a conical defect, reproducing the massive BMS$_3$ character. We perform the computation in both discrete and continuum geometry formulations, showing consistency between them. In the discrete case, we integrate out bulk degrees of freedom in a Regge gravity framework, while in the continuum, we construct a dual non-local boundary field theory encoding geodesic length fluctuations. Our study shows that the additional modes of the massive character, compared to the vacuum case, originate from the explicit breaking of radial diffeomorphism symmetry by the defect. This provides a concrete geometric mechanism in Regge gravity, tracing the appearance of massive BMS$_3$ particles to diffeomorphism breaking by conical defects, and highlights the broader relevance of discrete geometry approaches to quantum gravity with matter.

gr-qc↗

arXiv2024

Random Geometry and Quantum Spacetime: From scale-invariant random geometries and asymptotic safety to random hyperbolic surfaces and JT gravity

This thesis is driven by a central question: "What can we learn from random geometries about the structure of quantum spacetime?" In Chapter 2, we provide a partial review of the mathematical foundation of this thesis, random geometry. In Chapter 3, we use a construction coming from random geometry called Mating of Trees to build scale-invariant random geometries that appear in Liouville Quantum Gravity and have the potential to implement the UV fixed point predicted by Asymptotic Safety in two and three dimensions. In Chapter 4 we explore the random geometry formulation of JT gravity and how our understanding of random critical maps yields the discovery of a new family of deformations of JT gravity. Furthermore, the connection between JT gravity and matrix models leads us to delve deeper into the link between discrete geometry and hyperbolic surfaces, building upon the geometry of metric maps and irreducible metric maps in Chapter 5.

hep-th↗

arXiv2024

A relation between $(2,2m-1)$ minimal strings and the Virasoro minimal string

We propose a connection between the newly formulated Virasoro minimal string and the well-established $(2,2m-1)$ minimal string by deriving the string equation of the Virasoro minimal string using the expansion of its density of states in powers of $E^{m+1/2}$. This string equation is expressed as a power series involving double-scaled multicritical matrix models, which are dual to $(2,2m-1)$ minimal strings. This reformulation of Virasoro minimal strings enables us to employ matrix theory tools to compute its $n$-boundary correlators. We analyze the scaling behavior of $n$-boundary correlators and quantum volumes $V^{(b)}_{0,n}(\ell_1,\dots,\ell_n)$ in the JT gravity limit.

hep-th↗

arXiv2023

Critical JT Gravity

In this paper, we investigate a critical behavior of JT gravity, a model of two-dimensional quantum gravity on constant negatively curved spacetimes. Our approach involves using techniques from random maps to investigate the generating function of Weil--Petersson volumes, which count random hyperbolic surfaces with defects. The defects are weighted geodesic boundaries, and criticality is reached by tuning the weights to the regime where macroscopic holes emerge in the hyperbolic surface, namely \textit{non-generic criticality}. We analyze the impact of this critical regime on some universal features, such as its density of states. We present a family of models that interpolates between systems with $\rho_0(E)\sim\sqrt{E-E_0}$ and $\rho_0(E)\sim (E-E_0)^{3/2}$, which are commonly found in models of JT gravity coupled to dynamical end-of-the-world and FZZT branes, and give a precise definition of what this phase transition means from the random geometry point of view.

hep-th↗

arXiv2022

Scale-invariant random geometry from mating of trees: a numerical study

The search for scale-invariant random geometries is central to the Asymptotic Safety hypothesis for the Euclidean path integral in quantum gravity. In an attempt to uncover new universality classes of scale-invariant random geometries that go beyond surface topology, we explore a generalization of the mating of trees approach introduced by Duplantier, Miller and Sheffield. The latter provides an encoding of Liouville Quantum Gravity on the 2-sphere decorated by a certain random space-filling curve in terms of a two-dimensional correlated Brownian motion, that can be viewed as describing a pair of random trees. The random geometry of Liouville Quantum Gravity can be conveniently studied and simulated numerically by discretizing the mating of trees using the Mated-CRT maps of Gwynne, Miller and Sheffield. Considering higher-dimensional correlated Brownian motions, one is naturally led to a sequence of non-planar random graphs generalizing the Mated-CRT maps that may belong to new universality classes of scale-invariant random geometries. We develop a numerical method to efficiently simulate these random graphs and explore their possible scaling limits through distance measurements, allowing us in particular to estimate Hausdorff dimensions in the two- and three-dimensional setting. In the two-dimensional case these estimates accurately reproduce previous known analytic and numerical results, while in the three-dimensional case they provide a first window on a potential three-parameter family of new scale-invariant random geometries.

gr-qc↗

arXiv2021

Ceramic processing and multiferroic properties of the perovskite YMnO$_3$-BiFeO$_3$ binary system

The perovskite (1-x)YMnO$_3$-xBiFeO$_3$ binary system is very promising because of its multiferroic end members. Nanocrystalline phases have been recently obtained by mechanosynthesis across the system, and the perovskite structural evolution has been described. Two continuous solid solutions with orthorhombic Pnma and rhombohedral R3c symmetries were found, which coexist within a broad compositional interval of 0.5 < x < 0.9. This might be a polar-nonpolar morphotropic phase boundary region, at which strong phase-change magnetoelectric responses can be expected. A major issue is phase decomposition at moderate temperatures that highly complicates ceramic processing. This is required for carrying out a sound electrical characterization and also for their use in devices. We present here the application of Spark Plasma Sintering to the ceramic processing of YMnO$_3$-BiFeO$_3$ phases. This advanced technique, when combined with nanocrystalline powders, allowed densifying phases at reduced processing temperatures and times, so that perovskite decomposition was avoided. Electrical measurements were accomplished, and the response was shown to be mostly dominated by conduction. Nonetheless, the intrinsic dielectric permittivity was obtained, and a distinctive enhancement in the phase coexistence region was revealed. Besides, Rayleigh-type behaviour characteristic of ferroelectrics was also demonstrated for all rhombohedral phases. Magnetic characterization was performed in this region, and antiferromagnetism was shown.

cond-mat.mtrl-sci↗

arXiv2020

Renormalization Group Approach to the Continuum Limit of Matrix Models of Quantum Gravity with Preferred Foliation

This contribution is not intended as a review but, by suggestion of the editors, as a glimpse ahead into the realm of dually weighted tensor models for quantum gravity. This class of models allows one to consider a wider class of quantum gravity models, in particular one can formulate state sum models of spacetime with an intrinsic notion of foliation. The simplest one of these models is the one proposed by Benedetti and Henson, which is a matrix model formulation of two-dimensional Causal Dynamical Triangulations (CDT). In this paper we apply the Functional Renormalization Group Equation (FRGE) to the Benedetti-Henson model with the purpose of investigating the possible continuum limits of this class of models. Possible continuum limits appear in this FRGE approach as fixed points of the renormalization group flow where the size of the matrix acts as the renormalization scale. Considering very small truncations, we find fixed points that are compatible with analytically known results for CDT in two dimensions. By studying the scheme dependence of our results we find that precision results require larger truncations than the ones considered in the present work. We conclude that our work suggests that the FRGE is a useful exploratory tool for dually weighted matrix models. We thus expect that the FRGE will be a useful exploratory tool for the investigation of dually weighted tensor models for CDT in higher dimensions.

gr-qc↗

arXiv2014

Simulating Behaviours to face up an Emergency Evacuation

Computer based models describing pedestrian behavior in an emergency evacuation play a vital role in the development of active strategies that minimize the evacuation time when a closed area must be evacuated. The reference model has a hybrid structure where the dynamics of fire and smoke propagation are modeled by means of Cellular Automata and for simulating people's behavior we are using Intelligent Agents. The model consists of two sub-models, called environmental and pedestrian ones. As part of the pedestrian model, this paper concentrates in a methodology that is able to model some of the frequently observed human's behaviors in evacuation exercises. Each agent will perceive what is happening around, select the options that exist in that context and then it makes a decision that will reflect its ability to cope with an emergency evacuation, called in this work, behavior. We also developed simple exercises where the model is applied to the simulation of an evacuation due to a potential hazard, such as fire, smoke or some kind of collapse.

cs.OH↗