arXiv subjects

Daniel A. Stariolo

Publications and source records attributed to Daniel A. Stariolo.

At least 19 recordsLinked to original sources

arXiv2026

Zero-temperature dynamics of the spherical model with non-reciprocal interactions

We analytically solve the zero-temperature dynamics of the spherical model with non-reciprocal random interactions drawn from the real elliptic ensemble of random matrices, where a single parameter $η$ continuously interpolates between purely symmetric ($η=1$) and purely antisymmetric ($η=-1$) couplings. We show that the two-time correlation and response functions depend on both times in the presence of non-reciprocal interactions, reflecting the breakdown of time-translation invariance and the absence of equilibrium at long times. Nevertheless, the long-time relaxation of the two-time observables is governed by exponential decays, in contrast to the slow, power-law relaxation characteristic of the model with purely symmetric interactions. We further show that, when the interactions present antisymmetric correlations of strength $η<0$, there is a time scale $τ(η)$ above which the dynamics undergoes a transition to an oscillatory regime where the two-time observables display periodic oscillations with an exponentially decaying amplitude. Overall, our results give a detailed account of the dynamics of the spherical model with non-reciprocal interactions at zero temperature, providing a benchmark for the study of complex systems with nonlinear and asymmetric interactions.

cond-mat.stat-mech↗

arXiv2023

Finite-size relaxational dynamics of a spike random matrix spherical model

We present a thorough numerical analysis of the relaxational dynamics of the Sherrington-Kirkpatrick spherical model with an additive non-disordered perturbation for large but finite sizes $N$. In the thermodynamic limit and at low temperatures, the perturbation is responsible for a phase transition from a spin glass to a ferromagnetic phase. We show that finite size effects induce the appearance of a distinctive slow regime in the relaxation dynamics, the extension of which depends on the size of the system and also on the strength of the non-disordered perturbation. The long time dynamics is characterized by the two largest eigenvalues of a spike random matrix which defines the model, and particularly by the statistics of the gap between them. We characterize the finite size statistics of the two largest eignevalues of the spike random matrices in the different regimes, sub-critical, critical and super-critical, confirming some known results and anticipating others, even in the less studied critical regime. We also numerically characterize the finite size statistics of the gap, which we hope may encourage analytical work which is lacking. Finally, we compute the finite size scaling of the long time relaxation of the energy, showing the existence of power laws with exponents that depend on the strenght of the non-disordered perturbation, in a way which is governed by the finite size statistics of the gap.

cond-mat.dis-nn↗

arXiv2021

A branching random-walk model of disease outbreaks and the percolation backbone

The size and shape of the region affected by an outbreak is relevant to understand the dynamics of a disease and help to organize future actions to mitigate similar events. A simple extension of the SIR model is considered, where agents diffuse on a regular lattice and the disease may be transmitted when an infected and a susceptible agents are nearest neighbors. We study the geometric properties of both the connected cluster of sites visited by infected agents (outbreak cluster) and the set of clusters with sites that have not been visited. By changing the density of agents, our results show that there is a mixed-order (hybrid) transition where the region affected by the disease is finite in one phase but percolates through the system beyond the threshold. Moreover, the outbreak cluster seems to have the same exponents of the backbone of the critical cluster of the ordinary percolation while the clusters with unvisited sites have a size distribution with a Fisher exponent $τ<2$.

cond-mat.stat-mech↗

arXiv2021

Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model

We revisit the gradient descent dynamics of the spherical Sherrington-Kirkpatrick ($p=2$) model with finite number of degrees of freedom. For fully random initial conditions we confirm that the relaxation takes place in three time regimes: a first algebraic one controlled by the decay of the eigenvalue distribution of the random exchange interaction matrix at its edge in the infinite size limit; a faster algebraic one determined by the distribution of the gap between the two extreme eigenvalues; and a final exponential one determined by the minimal gap sampled in the disorder average. We also analyse the finite size effects on the relaxation from initial states which are almost projected on the saddles of the potential energy landscape, and we show that for deviations scaling as $N^{-ν}$ from perfect alignment the system escapes the initial configuration in a time-scale scaling as $\ln N$ after which the dynamics no longer "self-averages" with respect to the initial conditions. We prove these statements with a combination of analytic and numerical methods.

cond-mat.stat-mech↗

arXiv2020

Barriers, trapping times and overlaps between local minima in the dynamics of the disordered Ising $p$-spin Model

We study the low temperature out of equilibrium Monte Carlo dynamics of the disordered Ising $p$-spin Model with $p=3$ and a small number of spin variables. We focus on sequences of configurations that are stable against single spin flips obtained by instantaneous gradient descent from persistent ones. We analyze the statistics of energy gaps, energy barriers and trapping times on sub-sequences such that the overlap between consecutive configurations does not overcome a threshold. We compare our results to the predictions of various trap models finding the best agreement with the step model when the $p$-spin configurations are constrained to be uncorrelated.

cond-mat.dis-nn↗

arXiv2020

COVID-19 in air suspensions

We analyse the stability of virus-carrying particles in air at equilibrium after the dissipation of the initial turbulent process produced by sneezing, coughing, breathing or speaking. Because the viruses are expelled mainly attached to small droplets, with diverse sizes and weights, and the external environmental conditions can also be diverse, the subsequent motion spannes different spatial and temporal scales. For droplet sizes larger than $100\,μm$, computing the time of decay to the ground and the distance travelled with a simple free fall model with empirical data extracted from the literature, we obtain distances in the range between $1$ to $3$ meters from the emitter, with a falling time of less than $1\,s$, similar to known recommendations for safe social distancing. For droplets sizes less than $100\,μm$ a simple model of motion in a viscous medium predicts that isolated viruses could remain suspended in quiet air for more than a month, while small droplets of $1\,μm$ in size can remain suspended for several hours, in agreement with recent experimental results on virus stability in aerosols. These results give solid background for the discussion of prevention strategies, like the use of masks in closed environments.

physics.class-ph↗

arXiv2018

A three-state model with competing antiferromagnetic and pairing interactions

Motivated by the rich phase diagram of the high temperature superconductors, we introduce a toy model with three state variables which can be interpreted as two state particles and holes. The Hamiltonian has a term which favors antiferromagnetism and an additional competing interaction which favors bonding between pairs of antiparallel spins mediated by holes. For low concentration of holes the dominant interaction between particles has antiferromagnetic character, leading to an antiferromagnetic phase in the temperature-hole concentration phase diagram, qualitatively similar to the antiferromagnetic phase of doped Mott insulators. For growing concentration of holes antiferromagnetic order is weakend and a phase with a different kind of order mediated by holes appears. This last phase has the form of a dome in the T-hole concentration plane. The whole phase diagram resembles those of some families of high $T_c$ superconductors. We compute the phase diagram in the mean field approximation and characterize the different phase transitions through Monte Carlo simulations.

cond-mat.supr-con↗

arXiv2017

Quantum and thermal melting of stripe forming systems with competing long ranged interactions

We study the quantum melting of stripe phases in models with competing short range and long range interactions decaying with distance as $1/r^σ$ in two space dimensions. At zero temperature we find a two step disordering of the stripe phases with the growth of quantum fluctuations. A quantum critical point separating a phase with long range positional order from a phase with long range orientational order is found when $σ\leq 4/3$, which includes the Coulomb interaction case $σ=1$. For $σ> 4/3$ the transition is first order, which includes the dipolar case $σ=3$. Another quantum critical point separates the orientationally ordered (nematic) phase from a quantum disordered phase for any value of $σ$. Critical exponents as a function of $σ$ are computed at one loop order in an $ε$ expansion and, whenever available, compared with known results. For finite temperatures it is found that for $σ\geq 2$ orientational order decays algebraically with distance until a critical Kosterlitz-Thouless line. Nevertheless, for $σ< 2$ it is found that long range orientational order can exist at finite temperatures until a critical line which terminates at the quantum critical point at $T=0$. The temperature dependence of the critical line near the quantum critical point is determined as a function of $σ$.

cond-mat.stat-mech↗

arXiv2016

Pair correlations and structure factor of the $J_1$-$J_2$ square lattice Ising model in an external field within the Cluster Variation Method

We compute the structure factor of the $J_1$-$J_2$ Ising model in an external field on the square lattice within the Cluster Variation Method. We use a four point plaquette approximation, which is the minimal one able to capture phases with broken orientational order in real space, like the recently reported Ising-nematic phase in the model. The analysis of different local maxima in the structure factor allows us to track the different phases and phase transitions against temperature and external field. Although the nematic susceptibility is not directly related to the structure factor, we show that because of the close relationship between the nematic order parameter and the structure factor, the latter shows unambiguous signatures of the presence of a nematic phase, in agreement with results from direct minimization of a variational free energy. The disorder variety of the model is identified and the possibility that the CVM four point approximation be exact on the disorder variety is discussed.

cond-mat.stat-mech↗

arXiv2016

Modulated phases in external fields: when is reentrant behavior to be expected?

We introduce a new coarse grain model capable of describing the phase behavior of two dimensional ferromagnetic systems with competing exchange and dipolar interactions, as well as an external magnetic field. An improved expression for the mean field entropic contribution allows to compute the phase diagram in the whole temperature versus external field plane. We find that the topology of the phase diagram may be qualitatively different depending on the ratio between the strength of the competing interactions. In the regime relevant for ultrathin ferromagnetic films with perpendicular anisotropy we confirm the presence of inverse symmetry breaking from a modulated phase to a homogenous one as the temperature is lowered at constant magnetic field, as reported in experiments. For other values of the competing interactions we show that reentrance may be absent. Comparing thermodynamic quantities in both cases, as well as the evolution of magnetization profiles in the modulated phases, we conclude that the reentrant behavior is a consequence of the suppression of domain wall degrees of freedom at low temperatures at constant fields.

cond-mat.stat-mech↗

arXiv2015

Index statistical properties of sparse random graphs

Using the replica method, we develop an analytical approach to compute the characteristic function for the probability $\mathcal{P}_N(K,λ)$ that a large $N \times N$ adjacency matrix of sparse random graphs has $K$ eigenvalues below a threshold $λ$. The method allows to determine, in principle, all moments of $\mathcal{P}_N(K,λ)$, from which the typical sample to sample fluctuations can be fully characterized. For random graph models with localized eigenvectors, we show that the index variance scales linearly with $N \gg 1$ for $|λ| > 0$, with a model-dependent prefactor that can be exactly calculated. Explicit results are discussed for Erdös-Rényi and regular random graphs, both exhibiting a prefactor with a non-monotonic behavior as a function of $λ$. These results contrast with rotationally invariant random matrices, where the index variance scales only as $\ln N$, with an universal prefactor that is independent of $λ$. Numerical diagonalization results confirm the exactness of our approach and, in addition, strongly support the Gaussian nature of the index fluctuations.

cond-mat.stat-mech↗

arXiv2015

Nematic phase in the J$_1$-J$_2$ square lattice Ising model in an external field

The J$_1$-J$_2$ Ising model in the square lattice in the presence of an external field is studied by two approaches: the Cluster Variation Method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter $κ=J_2/|J_1|$ which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.

cond-mat.stat-mech↗

arXiv2015

Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions

We study two dimensional stripe forming systems with competing repulsive interactions decaying as $r^{-α}$. We derive an effective Hamiltonian with a short range part and a generalized dipolar interaction which depends on the exponent $α$. An approximate map of this model to a known XY model with dipolar interactions allows us to conclude that, for $α<2$ long range orientational order of stripes can exist in two dimensions, and establish the universality class of the models. When $α\geq 2$ no long-range order is possible, but a phase transition in the KT universality class is still present. These two different critical scenarios should be observed in experimentally relevant two dimensional systems like electronic liquids ($α=1$) and dipolar magnetic films ($α=3$). Results from Langevin simulations of Coulomb and dipolar systems give support to the theoretical results.

cond-mat.stat-mech↗

arXiv2014

Energy Landscape of the Finite-Size Mean-field 2-Spin Spherical Model and Topology Trivialization

Motivated by the recently observed phenomenon of topology trivialization of potential energy landscapes (PELs) for several statistical mechanics models, we perform a numerical study of the finite size $2$-spin spherical model using both numerical polynomial homotopy continuation and a reformulation via non-hermitian matrices. The continuation approach computes all of the complex stationary points of this model while the matrix approach computes the real stationary points. Using these methods, we compute the average number of stationary points while changing the topology of the PEL as well as the variance. Histograms of these stationary points are presented along with an analysis regarding the complex stationary points. This work connects topology trivialization to two different branches of mathematics: algebraic geometry and catastrophe theory, which is fertile ground for further interdisciplinary research.

cond-mat.stat-mech↗

arXiv2014

Inverse transition in the dipolar frustrated Ising ferromagnet: the role of domain walls

We present a theoretical study aimed to elucidate the origin of the inverse symmetry breaking transition observed in ultrathin magnetic films with perpendicular anisotropy. We study the behavior of the dipolar frustrated Ising model in a mean field approximation as well as two other models with simple domain walls. By a numerical analysis we show that the internal degrees of freedom of the domain walls are decisive for the presence of the inverse symmetry breaking transition. In particular, we show that in a sharp domain wall model the inverse transition is absent. At high temperatures the additional degrees of freedom of the extended domain walls increase the entropy of the system leading to a reduction of the free energy of the stripe phase. Upon lowering the temperature the domain walls become narrow and with the corresponding degrees of freedom effectively frozen, which eventually induces an inverse transition to the competing homogeneous phase. We also show that, for growing external field at constant temperature, the stripe width grows strongly when approaching the critical field line and diverges at the transition. These results indicate that the inverse transition is a continuous phase transition and that the domain wall profiles as well as the temperature has little effect on the critical behavior of the period of the domain as function of the applied field.

cond-mat.stat-mech↗

arXiv2013

The nematic phase in stripe forming systems within the self consistent screening approximation

We show that in order to describe the isotropic-nematic transition in stripe forming systems with isotropic competing interactions of the Brazovskii class it is necessary to consider the next to leading order in a 1/N approximation for the effective Hamiltonian. This can be conveniently accomplished within the self-consistent screening approximation. We solve the relevant equations and show that the self-energy in this approximation is able to generate the essential wave vector dependence to account for the anisotropic character of two-point correlation function characteristic of a nematic phase.

cond-mat.str-el↗

arXiv2013

Structure, diffusion and orientational freezing in lithium metasilicate

We report on the dynamic and structural characterization of lithium metasilicate $Li_2SiO_3$, a network forming ionic glass, by means of molecular dynamics simulations. The system is characterized by a network of $SiO_4$ tetrahedra disrupted by $Li$ ions which diffuse through the network. Measures of mean square displacement of $Si$ and $O$ atoms allow us to identify a temperature at which tetrahedra stop moving relative to each other. This temperature $T_c\approx 1500\,K$ can be characterized within the framework of mode coupling theory. At a much lower temperature $T_g\approx 1000\,K$, a change in the slope of the volume versus temperature data allows to single out the glass transition. We find signatures of both transitions in structural order parameters, related to the orientation of tetrahedra. Going down in temperature we find that, around the mode coupling transition temperature, a set of order parameters which measure the relative orientation of tetrahedra cease to increase and stay constant below $T_c$. Another well known measure of orientational order, the bond orientational order parameter, which in the studied system measures local order within single tetrahedrons, is found to continue growing below $T_c$ until $T_g$, below which it remains constant. Our results allow to relate two characteristic dynamic transitions with corresponding structural transitions, as observed in two different orientational order parameters. Furthermore, the results indicate that the network of thetrahedra continue to relax well below the point where neighboring tetrahedra cannot rearrange relative to each other, and the glass is reached only upon a process of relaxation of atoms which form the thetrahedron, as quantified by the change in the bond orientational order parameters.

cond-mat.soft↗

arXiv2013

Nematic Phase in two-dimensional frustrated systems with power law decaying interactions

We address the problem of orientational order in frustrated interaction systems as a function of the relative range of the competing interactions. We study a spin model Hamiltonian with short range ferromagnetic interaction competing with an antiferromagnetic component that decays as a power law of the distance between spins, $1/r^α$. These systems may develop a nematic phase between the isotropic disordered and stripe phases. We evaluate the nematic order parameter using a self-consistent mean field calculation. Our main result indicates that the nematic phase exists, at mean-field level, provided $0<α<4$. We analytically compute the nematic critical temperature and show that it increases with the range of the interaction, reaching its maximum near $α\sim 0.5$. We also compute a corse-grained effective Hamiltonian for long wave-length fluctuations. For $0<α<4$ the inverse susceptibility develops a set of continuous minima at wave vectors $|\vec k|=k_0(α)$ which dictate the long distance physics of the system. For $α\to 4$, $k_0\to 0$, making the competition between interactions ineffective for greater values of $α$.

cond-mat.stat-mech↗