arXiv subjects

Alessandro Codello

Publications and source records attributed to Alessandro Codello.

At least 19 recordsLinked to original sources

arXiv2026

Microscopic dynamics of consensus formation in multi-agent LLM Naming Games

Decentralized populations of Large Language Model (LLM) agents can spontaneously reach consensus on shared conventions, yet the microscopic mechanisms by which their internal stochasticity shapes macroscopic ordering remain unexplored. We study a minimal LLM Naming Game in which the listener's decision is a single-token LLM call at decoding temperature $T$, replacing the inventory check of the deterministic Naming Game. Each interaction decomposes into an in-inventory and an out-inventory channel with conditional rates $\pi(T)\!\equiv\!P(\text{YES}\mid w\in P_j)$ and $\phi(T)\!\equiv\!P(\text{YES}\mid w\notin P_j)$, whose balance controls an ordering-disordering drift. A mean-field theory of the two-rate dynamics yields an analytical ordering condition that generalizes the consensus threshold of the stochastic Naming Game to a critical line in the $(\pi,\phi)$ plane. Across three open-weight architectures, consensus is always reached, but through three distinct listener regimes: permissive (repaint-noise dominated), near-deterministic, and conservative (missed-collapse dominated). The effective finite-size exponent $\beta(T)$ in $t_{\rm conv}\!\sim\!N^{\beta}$ shifts with temperature, and the temperature-sensitivity $\alpha$ in $t_c\!\sim\!e^{\alpha T}$ ranges from ${\approx}\,0.67$ to ${\approx}\,0$ across architectures. Decoding temperature thus emerges as an architecture-dependent control parameter for decentralized LLM populations, quantitatively characterized by the statistical-physics toolkit.

physics.soc-ph↗

arXiv2026

A universal emulator for planar Ising lattices

We introduce the notion of an Ising emulator for two-dimensional Ising models: flat, unit-edge-length lattices can be represented as site- or bond-diluted supercells of a single host lattice, for which the Feynman--Vdovichenko/Kac--Ward solution is fixed once and for all. We construct explicit square and triangular emulators and show that a single transition matrix, supplemented by lattice-specific binary masks, gives all the thermodynamic quantities of interest for both ferro- and antiferromagnetic couplings. We apply the framework to all eleven Archimedean lattices, to all twenty $2$-uniform lattices -- whose thermodynamics is obtained here for the first time -- and to several pentagonal lattices, and show that the same construction extends directly to fractal and disordered Ising models, with no modification to the underlying machinery.

cond-mat.stat-mech↗

arXiv2026

The phase boundary of the random site Ising model

We introduce a new approach to disordered two-dimensional Ising models based on the extension of the combinatorial solution to randomized supercells. Applying it to the site-diluted Ising model on the square lattice, we resolve the full phase boundary $T_c(p)$ from the pure-Ising point to the percolation limit $T_c(p_c)=0$ with, in principle, arbitrary precision. The critical eigenvalue governing the transition is found to follow a remarkably accurate linear interpolation between the Ising and percolation endpoints, whose small but systematic deviations reveal the nontrivial fine structure of the phase boundary. Near the percolation threshold, we confirm the crossover exponent $\phi_{\rm RSIM}=1$ and extract the nonuniversal amplitude ${\alpha_{\rm RSIM}\simeq 1.616}$.

cond-mat.stat-mech↗

arXiv2025

Critical Temperature(s) of Sierpinski Carpet(s)

We present a key algorithmic improvement to the generalized combinatorial Feynman--Vdovichenko method for calculating the critical temperature of the Ising model on Sierpinski carpets $SC_k(a,b)$, originally introduced in arxiv:1505.02699. By reformulating the method in terms of purely real-valued transfer matrices, we substantially reduce their dimension. This optimization, together with modern computational resources, enables us to reach generation $k=10$ for the canonical $SC_k(3,1)$ carpet. Extrapolation from these data yields the most accurate estimate to date of the critical temperature $T_c^{(3,1)} = 1.4782927(26)$. We further extend the analysis to additional members of the $SC_k(a,b)$ family and report their corresponding critical temperatures.

cond-mat.stat-mech↗

arXiv2025

Bayesian Field Theory of the Rate Estimation

We address the statistical inference of a time-dependent rate of events in the framework of Bayesian field theory. This maps the problem to a Langevin equation which, beyond the local linear regime taken as reference, involves nonlinearities and an explicit dependence on the local shape of the maximum likelihood curve. We study the corresponding impacts in a perturbative expansion, formulating a scaling hypothesis for the order of shape corrections. We find that the pure nonlinearities dominate the mean and skewness. Crucially, we uncover that the leading correction to the variance is driven by noise propagation from the signal's effective curvature. We test the derived expansion with numerical simulations and illustrate its applicability on real neural spike data.

stat.ME↗

arXiv2022

Structural aspects of FRG in quantum tunnelling computations

We 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.

hep-th↗

arXiv2021

Multicritical hypercubic models

We study renormalization group multicritical fixed points in the $\epsilon$-expansion of scalar field theories characterized by the symmetry of the (hyper)cubic point group $H_N$. After reviewing the algebra of $H_N$-invariant polynomials and arguing that there can be an entire family of multicritical (hyper)cubic solutions with $\phi^{2n}$ interactions in $d=\frac{2n}{n-1}-\epsilon$ dimensions, we use the general multicomponent beta functionals formalism to study the special cases $d = 3-\epsilon$ and $d =\frac{8}{3}-\epsilon$, deriving explicitly the beta functions describing the flow of three- and four-critical (hyper)cubic models. We perform a study of their fixed points, critical exponents and quadratic deformations for various values of $N$, including the limit $N=0$, that was reported in another paper in relation to the randomly diluted single-spin models, and an analysis of the large $N$ limit, which turns out to be particularly interesting since it depends on the specific multicriticality. We see that, in general, the continuation in $N$ of the random solutions is different from the continuation coming from large-$N$, and only the latter interpolates with the physically interesting cases of low-$N$ such as $N=3$. Finally, we also include an analysis of a theory with quintic interactions in $d =\frac{10}{3}-\epsilon$ and, for completeness, the NNLO computations in $d=4-\epsilon$.

hep-th↗

arXiv2020

A multicritical Landau-Potts field theory

We investigate a perturbatively renormalizable $S_{q}$ invariant model with $N=q-1$ scalar field components below the upper critical dimension $d_c=\frac{10}{3}$. Our results hint at the existence of multicritical generalizations of the critical models of spanning random clusters and percolations in three dimensions. We also discuss the role of our multicritical model in a conjecture that involves the separation of first and second order phases in the $(d,q)$ diagram of the Potts model.

cond-mat.stat-mech↗

arXiv2020

On critical models with $N\leq 4$ scalars in $d=4-\epsilon$

We adopt a combination of analytical and numerical methods to study the renormalization group flow of the most general field theory with quartic interaction in $d=4-\epsilon$ with $N=3$ and $N=4$ scalars. For $N=3$, we find that it admits only three nondecomposable critical points: the Wilson-Fisher with $O(3)$ symmetry, the cubic with $H_3=(\mathbb{Z}_2)^3\rtimes S_3$ symmetry, and the biconical with $O(2)\times \mathbb{Z}_2$. For $N=4$, our analysis reveals the existence of new nontrivial solutions with discrete symmetries and with up to three distinct field anomalous dimensions.

hep-th↗

arXiv2020

The fate of $O(N)$ multi-critical universal behaviour

The multi-critical fixed points of $O(N)$ symmetric models cease to exist in the $N\to\infty$ limit, but the mechanism regulating their annihilation still presents several enigmatic aspects. Here, we explore the evolution of high-order multi-critical points in the $(d,N)$ plane and uncover a complex mosaics for their asymptotic behaviour at large $N$. This picture is confirmed by various RG approaches and constitutes a fundamental step towards the full comprehension of critical behaviour in $O(N)$ field theories.

cond-mat.stat-mech↗

arXiv2019

Symmetry and universality of multi-field interactions in $6-\epsilon$ dimensions

We outline a general strategy developed for the analysis of critical models, which we apply to obtain a heuristic classification of all universality classes with up to three field-theoretical scalar order parameters in $d=6-\epsilon$ dimensions. As expected by the paradigm of universality, each class is uniquely characterized by its symmetry group and by a set of its scaling properties, neither of which are built-in by the formalism but instead emerge nontrivially as outputs of our computations. For three fields, we find several solutions mostly with discrete symmetries. These are nontrivial conformal field theory candidates in less than six dimensions, one of which is a new perturbatively unitary critical model.

hep-th↗

arXiv2019

Criticality of Spin Systems with Weak Long-Range Interactions

The study of critical properties of systems with long-range interactions has attracted in the last 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 renormalization group, and we review their remarkable properties. For the sake of clarity and self-consistency, we start from the classical $O(N)$ spin models and we then move to quantum spin systems.

cond-mat.stat-mech↗

arXiv2019

Platonic Field Theories

We study renormalization group (RG) fixed points of scalar field theories endowed with the discrete symmetry groups of regular polytopes. We employ the functional perturbative renormalization group (FPRG) approach and the $\epsilon$-expansion in $d=d_c-\epsilon$. The upper critical dimensions relevant to our analysis are $d_c = 6,4,\frac{10}{3},3,\frac{14}{5},\frac{8}{3},\frac{5}{2},\frac{12}{5}$; in order to get access to the corresponding RG beta functions, we derive general multicomponent beta functionals $\beta_V$ and $\beta_Z$ in the aforementioned upper critical dimensions, most of which are novel. The field theories we analyze have $N=2$ (polygons), $N=3$ (Platonic solids) and $N=4$ (hyper-Platonic solids) field components. The main results of this analysis include a new candidate universality class in three physical dimensions based on the symmetry group $\mathbb{D}_5$ of the Pentagon. Moreover we find new Icosahedron fixed points in $d<3$, the fixed points of the $24$-Cell, multi-critical $O(N)$ and $\phi^n$-Cubic universality classes.

hep-th↗

arXiv2018

Leading order CFT analysis of multi-scalar theories in d>2

We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we just define to admit a Landau-Ginzburg description that includes the most general critical interactions built from monomials of the form $\phi_{i_1} \cdots \phi_{i_m}$. For all such models we analyze to the leading order of the $\epsilon$-expansion the anomalous dimensions of the fields and those of the composite quadratic operators. For models with even $m$ we extend the analysis to an infinite tower of composite operators of arbitrary order. The results are supplemented by the computation of some families of structure constants. We also find the equations which constrain the nontrivial critical theories at leading order and show that they coincide with the ones obtained with functional perturbative RG methods. This is done for the case $m=3$ as well as for all the even models. We ultimately specialize to $S_q$ symmetric models, which are related to the $q$-state Potts universality class, and focus on three realizations appearing below the upper critical dimensions $6$, $4$ and $\frac{10}{3}$, which can thus be nontrivial CFTs in three dimensions.

hep-th↗

arXiv2017

Functional RG approach to the Potts model

The critical behavior of the $(n+1)$-states Potts model in $d$-dimensions is studied with functional renormalization group techniques. We devise a general method to derive $\beta$-functions for continuos values of $d$ and $n$ and we write the flow equation for the effective potential (LPA) when instead $n$ is fixed. We calculate several critical exponents, which are found to be in good agreement with Monte Carlo simulations and $\epsilon$-expansion results available in the literature. In particular, we focus on Percolation $(n\to0)$ and Spanning Forest $(n\to-1)$ which are the only non-trivial universality classes in $d=4,5$ and where our methods converge faster.

cond-mat.stat-mech↗

arXiv2017

New universality class in three dimensions: The critical Blume-Capel model

We study the Blume-Capel universality class in $d=\frac{10}{3}-\epsilon$ dimensions. The RG flow is extracted by looking at poles in fractional dimension of three loop diagrams using $\overline{\rm MS}$. The theory is the only nontrivial universality class which admits an expansion to three dimensions with $\epsilon=\frac{1}{3}<1$. We compute the relevant scaling exponents and estimate some of the OPE coefficients to the leading order. Our findings agree with and complement CFT results. Finally we discuss a family of nonunitary multicritical models which includes the Lee-Yang and Blume-Capel classes as special cases.

hep-th↗

arXiv2017

Functional perturbative RG and CFT data in the $\epsilon$-expansion

We show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for a given universality class. The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. We illustrate our procedure in the $\epsilon$-expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multicritical models $\phi^{2n}$. Whenever comparison is possible our RG results explicitly match the ones recently derived in CFT frameworks.

hep-th↗

arXiv2017

Leading CFT constraints on multi-critical models in d>2

We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial $\phi^{m}$ below their upper critical dimensions $d_c=\frac{2m}{m-2}$, and study them using a combination of CFT constraints, Schwinger-Dyson equation and the free theory behavior at the upper critical dimension. For even integers $m \ge 4$ these theories coincide with the Landau-Ginzburg description of multi-critical phenomena and interpolate with the unitary minimal models in $d=2$, while for odd $m$ the theories are non-unitary and start at $m=3$ with the Lee-Yang universality class. For all the even potentials and for the Lee-Yang universality class, we show how the assumption of conformal invariance is enough to compute the scaling dimensions of the local operators $\phi^k$ and of some families of structure constants in either the coupling's or the $\epsilon$-expansion. For all other odd potentials we express some scaling dimensions and structure constants in the coupling's expansion.

hep-th↗