arXiv subjects

Miguel Aguilar-Janita

Publications and source records attributed to Miguel Aguilar-Janita.

5 recordsLinked to original sources

arXiv2026

Testing Replica Symmetry Breaking in the three-dimensional Edwards-Anderson model by using vanishing fields

Replica Symmetry Breaking (RSB) theory for spin glasses, which is exact in infinite dimensions, provides detailed predictions for the behavior of these systems. One of these predictions is that vanishing magnetic fields induce chaotic behavior. Here, vanishing has a precise meaning: we refer to an externally applied magnetic field with intensity scaling as $1/\sqrt{N}$, where $N$ is the number of spins in the system. RSB predicts that this chaotic behavior depends only on the probability density function of the overlap, $P(q)$, as computed at zero field. We proceed to test the RSB prediction in the 3D Edwards-Anderson model, by first computing the $P(q)$ numerically in the absence of a magnetic field. We then use this function as input to analytically compute the statistics of the states in the regime of a vanishing magnetic field, using a representation based on the Bolthausen-Sznitman coalescent process (which is exact for the mean-field Sherrington-Kirkpatrick model). This mixed numerical-analytical approach allows us to determine the prediction of RSB for the overlap distribution function measured in the presence of a small vanishing field, as well as the increase in chaoticity as the field strength grows. The above RSB predictions are quantitatively compared with the outcome of numerical simulations of the three-dimensional Edwards-Anderson in the presence of a small vanishing field, finding very good agreement. This agreement provides strong support for the idea that three-dimensional spin glass at zero magnetic field and low temperature is well described by RSB theory.

cond-mat.dis-nn↗

arXiv2024

Small field chaos in spin glasses: universal predictions from the ultrametric tree and comparison with numerical simulations

We study the chaotic behavior of the Gibbs state of spin-glasses under the application of an external magnetic field, in the crossover region where the field intensity scales proportional to $1/\sqrt{N}$, being $N$ the system size. We show that Replica Symmetry Breaking (RSB) theory provides universal predictions for chaotic behavior: they depend only on the zero-field overlap probability function $P(q)$ and are independent of other features of the system. Using solely $P(q)$ as input we can analytically predict quantitatively the statistics of the states in a small field. In the infinite volume limit, each spin-glass sample is characterized by an infinite number of states that have a tree-like structure. We generate the corresponding probability distribution through efficient sampling using a representation based on the Bolthausen-Sznitman coalescent. In this way, we can compute quantitatively properties in the presence of a magnetic field in the crossover region, the overlap probability distribution in the presence of a small field and the degree of decorrelation as the field is increased. To test our computations, we have simulated the Bethe lattice spin glass and the 4D Edwards-Anderson model, finding in both cases excellent agreement with the universal predictions.

cond-mat.dis-nn↗

arXiv2024

Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field

The very existence of a phase transition for spin glasses in an external magnetic field is controversial, even in high dimensions. We carry out massive simulations of the Ising spin-glass in a field, in six dimensions (which, according to classical -- but not generally accepted -- field-theoretical studies, is the upper critical dimension). We obtain results compatible with a second-order phase transition and estimate its critical exponents for the simulated lattice sizes. The detailed analysis performed by other authors of the replica symmetric Hamiltonian, under the hypothesis of critical behavior, predicts that the ratio of the renormalized coupling constants remain bounded as the correlation length grows. Our numerical results are in agreement with this expectation.

cond-mat.dis-nn↗

arXiv2024

Polarization-induced stress in the noisy voter model

A new model for the dynamics of opinion formation is proposed and analysed at the mean-field level. It can be regarded as a generalization of the noisy voter model in which agents update their binary states by copying others and by an intrinsic mechanism affected by the degree of polarization in the system. It also takes into account whether the agents enhance or reduce their intrinsic mechanism upon increasing polarization. Four phases or shapes of the steady-state probability of a fraction of agents in a given state are found (unimodal, bimodal, W and M). In the unimodal (resp. bimodal) phase, the copying (resp. intrinsic) mechanism is globally dominant, while in the W (resp. M) phase the copying (resp. intrinsic) mechanism is the relevant one close to the consensus states while it reduces its influence as approaching coexistence. In the thermodynamic limit, the bimodal and W phases disappear, while the unimodal and M phases prevail. The theoretical results, obtained analytically from the master equation, and the numerical simulations are in good agreement.

cond-mat.stat-mech↗

arXiv2023

Cooperation transitions in social games induced by aspiration-driven players

Cooperation and defection are social traits whose evolutionary origin is still unresolved. Recent behavioral experiments with humans suggested that strategy changes are driven mainly by the individuals' expectations and not by imitation. This work theoretically analyzes and numerically explores an aspiration-driven strategy updating in a well-mixed population playing games. The payoffs of the game matrix and the aspiration are condensed into just two parameters that allow a comprehensive description of the dynamics. We find continuous and abrupt transitions in the cooperation density with excellent agreement between theory and the Gillespie simulations. Under strong selection, the system can display several levels of steady cooperation or get trapped into absorbing states. These states are still relevant for experiments even when irrational choices are made due to their prolonged relaxation times. Finally, we show that for the particular case of the Prisoner Dilemma, where defection is the dominant strategy under imitation mechanisms, the self-evaluation update instead favors cooperation nonlinearly with the level of aspiration. Thus, our work provides insights into the distinct role between imitation and self-evaluation with no learning dynamics.

physics.soc-ph↗