arXiv subjects

F. Corberi

Publications and source records attributed to F. Corberi.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamic learning

We discuss the possibility to train a thermodynamic system, whose micro-variables are fully determined through the Hamiltonian by the usual statistical mechanical rules, to perform tasks such as memorization and generalization. Training is achieved by the application of suitable external fields, playing the role of {\it data}. At variance with conventional machine learning, no other logical or algorithmic rules are introduced. The system is amenable, in principle, to exact analytical calculations. We specialize this general approach to a prototypical Ising system with annealed dichotomous couplings and study its learning ability. Results indicate excellent memorization and good generalization capacity already for small systems, and a tendency to improve with system size.

cond-mat.stat-mech↗

arXiv2026

Coarsening in the long-range Persistent Voter Model

We investigate the coarsening kinetics in a long-range variant of the Persistent Voter Model in space dimensions $d=1$ and 2. In this model, agents can hold two confidence levels, normal and zealot. Normal agents imitate another opinion chosen at a distance $r$ with probability $P(r) \propto r^{-\alpha}$, with $\alpha >d$. On the contrary, while in the zealot state, agents keep their own opinion. Normal (zealot) agents can become zealots (normal) if their opinion is equal (different) to that of the chosen neighbour. Through numerical simulations we show that, for any values of $\alpha$, the model belongs to the same universality class of the long-range Ising model quenched to a small (non-zero) temperature, similarly to what was already known for the nearest-neighbor case. For the one-dimensional case, we further develop an analytical treatment, which reproduces the $\alpha$-dependence of the correlation length and the functional form of the correlation function. These results not only confirm that the introduction of opinion inertia mitigates the strong interfacial noise present in the Voter model, thus reinstating the basic kinetic mechanism of the Ising model, but also expand the applicability of this correspondence.

cond-mat.stat-mech↗

arXiv2025

Coarsening in the Persistent Voter Model: analytical results

We investigate the coarsening dynamics of a simplified version of the persistent voter model in which an agent can become a zealot -- i.e. resistent to change opinion -- at each step, based on interactions with its nearest neighbors. We show that such a model captures the main features of the original, non-Markovian, persistent voter model. We derive the governing equations for the one-point and two-point correlation functions. As these equations do not form a closed set, we employ approximate closure schemes, whose validity was confirmed through numerical simulations. Analytical solutions to these equations are obtained and well agree with the numerical results.

cond-mat.stat-mech↗

arXiv2020

Work fluctuations of self-propelled particles in the phase separated state

We study the large deviations of the distribution P(W_\tau) of the work associated with the propulsion of individual active brownian particles in a time interval \tau, in the region of the phase diagram where macroscopic phase separation takes place. P(W_\tau) is characterised by two peaks, associated to particles in the gaseous and in the clusterised phases, and two separate non-convex branches. Accordingly, the generating function of W_\tau cumulants displays a double singularity. We discuss the origin of such non-convex branches in terms of the peculiar dynamics of the system phases, and the relation between the observation time \tau and the typical persistence times of the particles in the two phases.

cond-mat.stat-mech↗

arXiv2017

Coarsening and percolation in the Ising Model with quenched disorder

Through large-scale numerical simulations, we study the phase ordering kinetics of the $2d$ Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important quantities -- the winding angle and the pair-connectedness -- we reveal the presence of a percolating structure in the pattern of domains. We focus on the pure case and on the random field and random bond Ising Model.

cond-mat.stat-mech↗

arXiv2014

Energy and Heat Fluctuations in a Temperature Quench

Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large $N$ model quenched below the critical temperature $T_C$. The main finding is that fluctuations exceeding a critical threshold do condense. Though driven by a mechanism similar to that of Bose-Einstein condensation, this phenomenon is an out-of-equilibrium feature produced by the breaking of energy equipartition occurring in the transient regime. The dynamical nature of the transition is illustrated by phase diagrams extending in the time direction.

cond-mat.stat-mech↗

arXiv2012

Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model

We study the nonconserved phase ordering dynamics of the d = 2, 3 random field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three di- mensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, the exponent in the preasymptotic power law is disorder-dependent, rather than being the one of the pure system. Furthermore, we find that the autocorre- lation function does not display superuniversal behavior. This restores consistency with previous results for the d = 1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random bond Ising model.

cond-mat.dis-nn↗

arXiv2011

Growth Law and Superuniversality in the Coarsening of Disordered Ferromagnets

We present comprehensive numerical results for domain growth in the two-dimensional {\it Random Bond Ising Model} (RBIM) with nonconserved Glauber kinetics. We characterize the evolution via the {\it domain growth law}, and two-time quantities like the {\it autocorrelation function} and {\it autoresponse function}. Our results clearly establish that the growth law shows a crossover from a pre-asymptotic regime with "power-law growth with a disorder-dependent exponent" to an asymptotic regime with "logarithmic growth". We compare this behavior with previous results on one-dimensional disordered systems and we propose a unifying picture in a renormalization group framework. We also study the corresponding crossover in the scaling functions for the two-time quantities. Super-universality is found not to hold. Clear evidence supporting the dimensionality dependence of the scaling exponent of the autoresponse function is obtained.

cond-mat.stat-mech↗

arXiv2010

Non-equilibrium critical properties of the Ising model on product graphs

We study numerically the non-equilibrium critical properties of the Ising model defined on direct products of graphs, obtained from factor graphs without phase transition (Tc = 0). On this class of product graphs, the Ising model features a finite temperature phase transition, and we find a pattern of scaling behaviors analogous to the one known on regular lattices: Observables take a scaling form in terms of a function L(t) of time, with the meaning of a growing length inside which a coherent fractal structure, the critical state, is progressively formed. Computing universal quantities, such as the critical exponents and the limiting fluctuation-dissipation ratio X_\infty, allows us to comment on the possibility to extend universality concepts to the critical behavior on inhomogeneous substrates.

cond-mat.stat-mech↗

arXiv2009

Phase ordering and universality for continuous symmetry models on graphs

We study the phase-ordering kinetics following a temperature quench of O(N) continuous symmetry models with and 4 on graphs. By means of extensive simulations, we show that the global pattern of scaling behaviours is analogous to the one found on usual lattices. The exponent a for the integrated response function and the exponent z, describing the growing length, are related to the large scale topology of the networks through the spectral dimension and the fractal dimension alone, by means of the same expressions as are provided by the analytic solution of the inifnite N limit. This suggests that the large N value of these exponents could be exact for every N.

cond-mat.stat-mech↗

arXiv2009

Complex phase-ordering of the one-dimensional Heisenberg model with conserved order parameter

We study the phase-ordering kinetics of the one-dimensional Heisenberg model with conserved order parameter, by means of scaling arguments and numerical simulations. We find a rich dynamical pattern with a regime characterized by two distinct growing lengths. Spins are found to be coplanar over regions of a typical size $L_V(t)$, while inside these regions smooth rotations associated to a smaller length $L_C(t)$ are observed. Two different and coexisting ordering mechanisms are associated to these lengths, leading to different growth laws $L_V(t)\sim t^{1/3}$ and $L_C(t)\sim t^{1/4}$ violating dynamical scaling.

cond-mat.stat-mech↗

arXiv2009

Fluctuation relations in non-equilibrium stationary states of Ising models

Fluctuation relations for the entropy production in non equilibrium stationary states of Ising models are investigated by Monte Carlo simulations. Systems in contact with heat baths at two different temperatures or subject to external driving will be studied. In the first case, by considering different kinetic rules and couplings with the baths, the behavior of the probability distributions of the heat exchanged in a time $τ$ with the thermostats, both in the disordered and in the low temperature phase, are discussed. The fluctuation relation is always verified in the large $τ$ limit and deviations from linear response theory are observed. Finite-$τ$ corrections are shown to obey a scaling behavior. In the other case the system is in contact with a single heat bath but work is done by shearing it. Also for this system the statistics collected for the mechanical work shows the validity of the fluctuation relation and preasymptotic corrections behave analogously to the case with two baths.

cond-mat.stat-mech↗

arXiv2008

Heat fluctuations in Ising models coupled with two different heat baths

Monte Carlo simulations of Ising models coupled to heat baths at two different temperatures are used to study a fluctuation relation for the heat exchanged between the two thermostats in a time $τ$. Different kinetics (single--spin--flip or spin--exchange Kawasaki dynamics), transition rates (Glauber or Metropolis), and couplings between the system and the thermostats have been considered. In every case the fluctuation relation is verified in the large $τ$ limit, both in the disordered and in the low temperature phase. Finite-$τ$ corrections are shown to obey a scaling behavior.

cond-mat.stat-mech↗

arXiv2008

Influence of thermal fluctuations on the geometry of the interfaces of the quenched Ising model

We study the role of the quench temperature $T_f$ in the phase-ordering kinetics of the Ising model with single spin flip in $d=2,3$. Equilibrium interfaces are flat at $T_f=0$, whereas at $T_f>0$ they are curved and rough (above the roughening temperature in $d=3$). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent $z=2$ of the size of domains $L(t)\sim t^{1/z}$ is unaffected by $T_f$, other exponents related to the interface geometry take different values at $T_f=0$ or $T_f>0$. For $T_f>0$ a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at $T_f=0$, to the asymptotic regime with curved interfaces characteristic of $T_f>0$. Furthermore, it is shown that the roughening length, although sub-dominant with respect to $L(t)$, produces appreciable correction to scaling up to very long times in $d=2$.

cond-mat.stat-mech↗

arXiv2008

Nonlinear susceptibilities and the measurement of a cooperative length

We derive the exact beyond-linear fluctuation dissipation relation, connecting the response of a generic observable to the appropriate correlation functions, for Markov systems. The relation, which takes a similar form for systems governed by a master equation or by a Langevin equation, can be derived to every order, in large generality with respect to the considered model, in equilibrium and out of equilibrium as well. On the basis of the fluctuation dissipation relation we propose a particular response function, namely the second order susceptibility of the two-particle correlation function, as an effective quantity to detect and quantify cooperative effects in glasses and disordered systems. We test this idea by numerical simulations of the Edwards-Anderson model in one and two dimensions.

cond-mat.stat-mech↗

arXiv2007

Phase-ordering kinetics on graphs

We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For each structure we discuss the scaling properties and compute the dynamical exponents. We show that the exponent $a_χ$ for the integrated response function, at variance with all the other exponents, is independent on temperature and on the presence of pinning. This universal character suggests a strict relation between $a_χ$ and the topological properties of the networks, in analogy to what observed on regular lattices.

cond-mat.stat-mech↗

arXiv2006

Aging dynamics and the topology of inhomogenous networks

We study phase ordering on networks and we establish a relation between the exponent $a_χ$ of the aging part of the integrated autoresponse function $χ_{ag}$ and the topology of the underlying structures. We show that $a_χ>0$ in full generality on networks which are above the lower critical dimension $d_L$, i.e. where the corresponding statistical model has a phase transition at finite temperature. For discrete symmetry models on finite ramified structures with $T_c = 0$, which are at the lower critical dimension $d_L$, we show that $a_χ$ is expected to vanish. We provide numerical results for the physically interesting case of the $2-d$ percolation cluster at or above the percolation threshold, i.e. at or above $d_L$, and for other networks, showing that the value of $a_χ$ changes according to our hypothesis. For $O({\cal N})$ models we find that the same picture holds in the large-${\cal N}$ limit and that $a_χ$ only depends on the spectral dimension of the network.

cond-mat.stat-mech↗

arXiv2002

The segregation of sheared binary fluids in the Bray-Humayun model

The phase separation process which follows a sudden quench inside the coexistence region is considered for a binary fluid subjected to an applied shear flow. This issue is studied in the framework of the convection-diffusion equation based on a Ginzburg-Landau free energy functional in the approximation scheme introduced by Bray and Humayun [{\it Phys.Rev.Lett.} {\bf 68}, 1559, (1992)]. After an early stage where domains form and shear effects become effective the system enters a scaling regime where the typical domains sizes $L_\parallel $, $L_\perp$ along the flow and perpendicular to it grow as $t^{5/4}$ and $t^{1/4}$. The structure factor is characterized by the existence of four peaks, similarly to previous theoretical and experimental observations, and by exponential tails at large wavevectors.

cond-mat.soft↗