arXiv subjects

Riccardo Ben Alì Zinati

Publications and source records attributed to Riccardo Ben Alì Zinati.

9 recordsLinked to original sources

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 $ϕ_{\rm RSIM}=1$ and extract the nonuniversal amplitude ${α_{\rm RSIM}\simeq 1.616}$.

cond-mat.stat-mech↗

arXiv2026

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↗

arXiv2022

Essential renormalisation group

We propose a novel scheme for the exact renormalisation group motivated by the desire of reducing the complexity of practical computations. The key idea is to specify renormalisation conditions for all inessential couplings, leaving us with the task of computing only the flow of the essential ones. To achieve this aim, we utilise a renormalisation group equation for the effective average action which incorporates general non-linear field reparameterisations. A prominent feature of the scheme is that, apart from the renormalisation of the mass, the propagator evaluated at any constant value of the field maintains its unrenormalised form. Conceptually, the simplifications can be understood as providing a description based only on quantities that enter expressions for physical observables since the redundant, non-physical content is automatically disregarded. To exemplify the scheme's utility, we investigate the Wilson-Fisher fixed point in three dimensions at order two in the derivative expansion. In this case, the scheme removes all order $\partial^2$ operators apart from the canonical term. Further simplifications occur at higher orders in the derivative expansion. Although we concentrate on a minimal scheme that reduces the complexity of computations, we propose more general schemes where inessential couplings can be tuned to optimise a given approximation. We further discuss the applicability of the scheme to a broad range of physical theories.

hep-th↗

arXiv2022

Dense polar active fluids in a disordered environment

We examine the influence of quenched disorder on the flocking transition of dense polar active matter. We consider incompressible systems of active particles with aligning interactions under the effect of either quenched random forces or random dilution. The system displays a continuous disorder-order (flocking) transition, and the associated scaling behavior is described by a new universality class which is controlled by a quenched Navier-Stokes fixed point. We determine the critical exponents through a perturbative renormalization group analysis. We show that the two forms of quenched disorder, random force and random mass (dilution), belong to the same universality class, in contrast with the situation at equilibrium.

cond-mat.stat-mech↗

arXiv2021

Stochastic dynamics of chemotactic colonies with logistic growth

The interplay between cellular growth and cell-cell signaling is essential for the aggregation and proliferation of bacterial colonies, as well as for the self-organization of cell tissues. To investigate this interplay, we focus here on the collective properties of dividing chemotactic cell colonies by studying their long-time and large-scale dynamics through a renormalization group (RG) approach. The RG analysis reveals that a relevant but unconventional chemotactic interaction -- corresponding to a polarity-induced mechanism -- is generated by fluctuations at macroscopic scales, even when an underlying mechanism is absent at the microscopic level. This emerges from the interplay of the well-known Keller--Segel (KS) chemotactic nonlinearity and cell birth and death processes. At one-loop order, we find no stable fixed point of the RG flow equations. We discuss a connection between the dynamics investigated here and the celebrated Kardar--Parisi--Zhang (KPZ) equation with long-range correlated noise, which points at the existence of a strong-coupling, nonperturbative fixed point.

cond-mat.stat-mech↗

arXiv2021

Multicritical hypercubic models

We study renormalization group multicritical fixed points in the $ε$-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 $ϕ^{2n}$ interactions in $d=\frac{2n}{n-1}-ε$ dimensions, we use the general multicomponent beta functionals formalism to study the special cases $d = 3-ε$ and $d =\frac{8}{3}-ε$, 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 $d =\frac{10}{3}-ε$ and, for completeness, the NNLO computations in $d=4-ε$.

hep-th↗

arXiv2020

Nonequilibrium polarity-induced mechanism for chemotaxis: emergent Galilean symmetry and exact scaling exponents

A generically observed mechanism that drives the self-organization of living systems is interaction via chemical signals among the individual elements -- which may represent cells, bacteria, or even enzymes. Here we propose a novel mechanism for such interactions, in the context of chemotaxis, which originates from the polarity of the particles and which generalizes the well-known Keller--Segel interaction term. We study the resulting large-scale dynamical properties of a system of such chemotactic particles using the exact stochastic formulation of Dean and Kawasaki along with dynamical renormalization group analysis of the critical state of the system. At this critical point, an emergent "Galilean" symmetry is identified, which allows us to obtain the dynamical scaling exponents exactly; these exponents reveal superdiffusive density fluctuations and non-Poissonian number fluctuations. We expect our results to shed light on how molecular regulation of chemotactic circuits can determine large-scale behavior of cell colonies and tissues.

cond-mat.stat-mech↗

arXiv2020

RG and logarithmic CFT multicritical properties of randomly diluted Ising models

We discuss how a spin system, which is subject to quenched disorder, might exhibit multicritical behaviors at criticality if the distribution of the impurities is arbitrary. In order to provide realistic candidates for such multicritical behaviors, we discuss several generalizations of the standard randomly diluted Ising's universality class adopting the $ε$-expansion close to several upper critical dimensions. In the presentation, we spend a special effort in bridging between CFT and RG results and discuss in detail the computation of quantities, which are of prominent interest in the case of logarithmic CFT.

hep-th↗