arXiv subjects

Federico Corberi

Publications and source records attributed to Federico Corberi.

At least 37 records · Page 2Linked to original sources

arXiv2021

How many phases nucleate in the bidimensional Potts model?

We study the kinetics of the two-dimensional q > 4-state Potts model after a shallow quench slightly below the critical temperature and above the pseudo spinodal. We use numerical methods and we focus on intermediate values of q, 4 < q < 100. We show that, initially, the system evolves as if it were quenched to the critical temperature. The further decay from the metastable state occurs by nucleation of k out of the q possible phases. For a given quench temperature, k is a logarithmically increasing function of the system size. This unusual finite size dependence is a consequence of a scaling symmetry underlying the nucleation phenomenon for these parameters.

cond-mat.stat-mech↗

arXiv2020

Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures

We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling: $J(r) \sim r^{-(d+σ)}$, where $d=2$ is the dimensionality. According to the Bray-Rutenberg predictions, the exponent $σ$ controls the algebraic growth in time of the characteristic domain size $L(t)$, $L(t) \sim t^{1/z}$, with growth exponent $z=1+σ$ for $σ<1$ and $z=2$ for $σ>1$. These results hold for quenches to a non-zero temperature $T>0$ below the critical temperature $T_c$. We show that, in the case of quenches to $T=0$, due to the long-range interactions, the interfaces experience a drift which makes the dynamics of the system peculiar. More precisely we find that in this case the growth exponent takes the value $z=4/3$, independent of $σ$, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for simplified models.

cond-mat.stat-mech↗

arXiv2020

The interplay between phase-separation and gene-enhancer communication: a theoretical study

The phase-separation occurring in a system of mutually interacting proteins that can bind on specific sites of a chromatin fiber is here investigated. This is achieved by means of extensive Molecular Dynamics simulations of a simple polymer model which includes regulatory proteins as interacting spherical particles. Our interest is particularly focused on the role played by phase-separation in the formation of molecule aggregates that can join distant regulatory elements, such as gene promoters and enhancers, along the DNA. We find that the overall equilibrium state of the system resulting from the mutual interplay between binding molecules and chromatin can lead, under suitable conditions that depend on molecules concentration, molecule-molecule and molecule-DNA interactions, to the formation of phase-separated molecular clusters allowing robust contacts between regulatory sites. Vice-versa, the presence of regulatory sites can promote the phase-separation process. Different dynamical regimes can generate the enhancer-promoter contact, either by cluster nucleation at binding sites or by bulk spontaneous formation of the mediating cluster to which binding sites are successively attracted. The possibility that such processes can explain experimental live-cell imaging data measuring distances between regulatory sites during time is also discussed.

cond-mat.soft↗

arXiv2020

Quasi-deterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets

We discuss the interplay between the degree of dynamical stochasticity, memory persistence and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory effects, which correspond to the slowest possible temporal decay of the correlation function, are accompanied by the largest possible violation of self-averaging and a quasi-deterministic descent into the ergodic components. This phenomenon is observed in different systems, such as the Ising model with long-range interactions, including mean-field, and the short-range random field Ising model.

cond-mat.stat-mech↗

arXiv2020

Growth Kinetics and Aging Phenomena in a Frustrated System

We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links $a$ can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in a radical way. Small $a$ does not prevent the system from a complete ordering, but this occurs in an extremely (logarithmically) slow manner. However, larger values of this parameter destroy complete ordering, due to frustration, and the evolution is comparatively faster (algebraic). Our study shows a precise correspondence between the kind of developing order, ferromagnetic versus frustrated, and the speed of evolution. The aging properties of the system are studied by focusing on the scaling properties of two-time quantities, the autocorrelation and linear response functions. We find that the contribution of equilibrium and an aging part to these functions occurs differently in the various regions of the phase diagram of the model. When quenching inside the ferromagnetic phase, the two-time quantities are obtained by the addition of these parts. Instead, in the paramagnetic phase, these two contributions enter multiplicatively. Both of the scaling forms are shown with excellent accuracy, and the corresponding scaling functions and exponents have been determined and discussed.

cond-mat.stat-mech↗

arXiv2020

Dynamics of fluctuations in the Gaussian model with dissipative Langevin Dynamics

We study the dynamics of the fluctuations of the variance $s$ of the order parameter of the Gaussian model, following a temperature quench of the thermal bath. At each time $t$, there is a critical value $s_c(t)$ of $s$ such that fluctuations with $s>s_c(t)$ are realized by condensed configurations of the systems, i.e., a single degree of freedom contributes macroscopically to $s$. This phenomenon, which is closely related to the usual condensation occurring on average quantities, is usually referred to as {\it condensation of fluctuations}. We show that the probability of fluctuations with $s<\inf_t [s_c(t)]$, associated to configurations that never condense, after the quench converges rapidly and in an adiabatic way towards the new equilibrium value. The probability of fluctuations with $s>\inf_t [s_c(t)]$, instead, displays a slow and more complex behavior, because the macroscopic population of the condensing degree of freedom is involved.

cond-mat.stat-mech↗

arXiv2019

Emergence of correlations in highly biased Consensus Models in seed initial configuration

We study the consensus probability in Voter Model and Invasion Process starting from a seed initial configuration. In the case where the opinions have the same strength or slightly different (weak bias) this function was computed analytically by Sood, Antal and Redner and depends only on the degree of the promoter individual. We check numerically through large scale simulations the above mentioned theory and we find that in the case of strong bias a correlation between the consensus probability and other centrality measures emerge and Sood et al's theory is broken.

cond-mat.stat-mech↗

arXiv2019

Multinucleation in the first-order phase transition of the 2d Potts model

Using large-scale numerical simulations we studied the kinetics of the 2d q-Potts model for q > 4 after a shallow subcritical quench from a high-temperature homogeneous configuration. This protocol drives the system across a first-order phase transition. The initial state is metastable after the quench and, for final temperatures close to the critical one, the system escapes from it via a multi-nucleation process. The ensuing relaxation towards equilibrium proceeds through coarsening with competition between the equivalent ground states. This process has been analyzed for different choices of the parameters such as the number of states and the final quench temperature.

cond-mat.stat-mech↗

arXiv2019

Dynamics of fluctuations in the Gaussian model with conserved dynamics

We study the fluctuations of the Gaussian model, with conservation of the order parameter, evolving in contact with a thermal bath quenched from inverse temperature $β_i$ to a final one $β_f$. At every time there exists a critical value $s_c(t)$ of the variance $s$ of the order parameter per degree of freedom such that the fluctuations with $s>s_c(t)$ are characterized by a macroscopic contribution of the zero wavevector mode, similarly to what occurs in an ordinary condensation transition. We show that the probability of fluctuations with $s<\inf_t [s_c(t)]$, for which condensation never occurs, rapidly converges towards a stationary behavior. By contrast, the process of populating the zero wavevector mode of the variance, which takes place for $s>\inf _t [s_c(t)]$, induces a slow non-equilibrium dynamics resembling that of systems quenched across a phase transition.

cond-mat.stat-mech↗

arXiv2019

Universality in the time correlations of the long-range 1d Ising model

The equilibrium and nonequilibrium properties of ferromagnetic systems may be affected by the long-range nature of the coupling interaction. Here we study the phase separation process of a one-dimensional Ising model in the presence of a power-law decaying coupling, $J(r)=1/r^{1+σ}$ with $σ>0$, and we focus on the two-time autocorrelation function $C(t,t_w)=\langle s_i(t) s_i(t_w)\rangle$. We find that it obeys the scaling form $C(t,t_w)=f(L(t_w)/L(t))$, where $L(t)$ is the typical domain size at time $t$, and where $f(x)$ can only be of two types. For $σ>1$, when domain walls diffuse freely, $f(x)$ falls in the nearest-neighbour (nn) universality class. Conversely, for $σ\le 1$, when domain walls dynamics is driven, $f(x)$ displays a new universal behavior. In particular, the so-called Fisher-Huse exponent, which characterizes the asymptotic behavior of $f(x)\simeq x^{-λ}$ for $x\gg 1$, is $λ=1$ in the nn universality class ($σ> 1$) and $λ=1/2$ for $σ\le 1$.

cond-mat.stat-mech↗

arXiv2019

One dimensional phase-ordering in the Ising model with space decaying interactions

The study of the phase ordering kinetics of the ferromagnetic one-dimensional Ising model dates back to 1963 for non conserved order parameter (NCOP) and to 1991 for conserved order parameter (COP). The case of long range interactions $J(r)$ has been widely studied at equilibrium but their effect on relaxation is a much less investigated field. Here we make a detailed numerical and analytical study of both cases, NCOP and COP. Many results are valid for any positive, decreasing coupling $J(r)$, but we focus specifically on the exponential case, $J_{exp}(r)=e^{-r/R}$ with varying $R>0$, and on the integrable power law case, $J_{pow}(r) =1/r^{1+σ}$ with $σ> 0$. We find that the {\it asymptotic} growth law $L(t)$ is the usual algebraic one, $L(t)\sim t^{1/z}$, of the corresponding model with nearest neighborg interaction ($z_{NCOP}=2$ and $z_{COP}=3$) for all models except $J_{pow}$ for small $σ$: in the non conserved case when $σ\le 1$ ($z_{NCOP}=σ+1$) and in the conserved case when $σ\to 0^+$ ($z_{COP}=4β+3$, where $β=1/T$ is the inverse of the absolute temperature). The models with space decaying interactions also differ markedly from the ones with nearest neighbors due to the presence of many long-lasting preasymptotic regimes, such as an exponential mean-field behavior with $L(t)\sim e^{t}$, a ballistic one with $L(t)\sim t$, a slow (logarithmic) behavior $L(t)\sim \ln t$ and one with $L(t)\sim t^{1/σ+1}$. All these regimes and their validity ranges have been found analytically and verified in numerical simulations. Our results show that the main effect of the conservation law is a strong slowdown of COP dynamics if interactions have an extended range. Finally, we compare the Ising model at hand with continuum approaches based on a Ginzburg-Landau free energy.

cond-mat.stat-mech↗

arXiv2019

Probability distributions with singularities

In this paper we review some general properties of probability distributions which exibit a singular behavior. After introducing the matter with several examples based on various models of statistical mechanics, we discuss, with the help of such paradigms, the underlying mathematical mechanism producing the singularity and other topics such as the condensation of fluctuations, the relationships with ordinary phase-transitions, the giant response associated to anomalous fluctuations, and the interplay with Fluctuation Relations.

cond-mat.stat-mech↗

arXiv2019

Effects of Frustration on Fluctuation-dissipation Relations

We study numerically the aging properties of the two-dimensional Ising model with quenched disorder considered in our recent paper [Phys. Rev. E 95, 062136 (2017)], where frustration can be tuned by varying the fraction a of antiferromagnetic interactions. Specifically we focus on the scaling properties of the autocorrelation and linear response functions after a quench of the model to a low temperature. We find that the interplay between equilibrium and aging occurs differently in the various regions of the phase diagram of the model. When the quench is made into the ferromagnetic phase the two-time quantities are made by the sum of an equilibrium and an aging part, whereas in the paramagnetic phase these parts combine in a multiplicative way. Scaling forms are shown to be obeyed with good accuracy, and the corresponding exponents and scaling functions are determined and discussed in the framework of what is known in clean and disordered systems.

cond-mat.stat-mech↗

arXiv2018

Fractal character of the phase ordering kinetics of a diluted ferromagnet

We study numerically the coarsening kinetics of a two-dimensional ferromagnetic system with aleatory bond dilution. We show that interfaces between domains of opposite magnetisation are fractal on every lengthscale, but with different properties at short or long distances. Specifically, on lengthscales larger than the typical domains' size the topology is that of critical random percolation, similarly to what observed in clean systems or models with different kinds of quenched disorder. On smaller lengthscales a dilution dependent fractal dimension emerges. The Hausdorff dimension increases with increasing dilution $d$ up to the value $4/3$ expected at the bond percolation threshold $d=1/2$. We discuss how such different geometries develop on different lengthscales during the phase-ordering process and how their simultaneous presence determines the scaling properties of observable quantities.

cond-mat.stat-mech↗

arXiv2017

Large fluctuations and dynamic phase transition in a system of self-propelled particles

We study the statistics, in stationary conditions, of the work $W_τ$ done by the active force in different systems of self-propelled particles in a time $τ$. We show the existence of a critical value $W_τ^†$ such that fluctuations with $W_τ>W_τ^†$ correspond to configurations where interaction between particles plays a minor role whereas those with $W_τ< W_τ^†$ represent states with single particles dragged by clusters. This two-fold behavior is fully mirrored by the probability distribution $P(W_τ)$ of the work, which does not obey the large-deviation principle for $W_τ<W_τ^†$. This pattern of behavior can be interpreted as due to a phase transition occurring at the level of fluctuating quantities and an order parameter is correspondingly identified.

cond-mat.stat-mech↗

arXiv2017

Effective mobility and diffusivity in coarsening processes

We suggest that coarsening dynamics can be described in terms of a generalized random walk, with the dynamics of the growing length $L(t)$ controlled by a drift term, $μ(L)$, and a diffusive one, ${\cal D}(L)$. We apply this interpretation to the one dimensional Ising model with a ferromagnetic coupling constant decreasing exponentially on the scale $R$. In the case of non conserved (Glauber) dynamics, both terms are present and their balance depend on the interplay between $L(t)$ and $R$. In the case of conserved (Kawasaki) dynamics, drift is negligible, but ${\cal D}(L)$ is strongly dependent on $L$. The main pre-asymptotic regime displays a speeding of coarsening for Glauber dynamics and a slowdown for Kawasaki dynamics. We reason that a similar behaviour can be found in two dimensions.

cond-mat.stat-mech↗

arXiv2017

Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration

We study numerically a two-dimensional random-bond Ising model where frustration can be tuned by varying the fraction $a$ of antiferromagnetic coupling constants. At low temperatures the model exhibits a phase with ferromagnetic order for sufficiently small values of $a$, $a a_a$ an antiferromagnetic phase exists. After a deep quench from high temperatures, slow evolution is observed for any value of $a$. We show that different amounts of frustration, tuned by $a$, affect the dynamical properties in a highly non trivial way. In particular, the kinetics is logarithmically slow in phases with ferromagnetic or antiferromagnetic order, whereas evolution is faster, i.e. algebraic, when spin glass order is prevailing. An interpretation is given in terms of the different nature of phase space.

cond-mat.stat-mech↗

arXiv2017

Development and regression of a large fluctuation

We study the evolution leading to (or regressing from) a large fluctuation in a Statistical Mechanical system. We introduce and study analytically a simple model of many identically and independently distributed microscopic variables $n_m$ ($m=1,M$) evolving by means of a master equation. We show that the process producing a non-typical fluctuation with a value of $N=\sum_{m=1}^Mn_m$ well above the average $\langle N\rangle$ is slow. Such process is characterized by the power-law growth of the largest possible observable value of $N$ at a given time $t$. We find similar features also for the reverse process of the regression from a rare state with $N\gg \langle N\rangle$ to a typical one with $N \simeq \langle N\rangle$.

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