Mean Field Research Articles

One point functions in large N vector models at finite chemical potential

Abstract We evaluate the thermal one point function of higher spin currents in the critical model of U(N) complex scalars interacting with a quartic potential and the U(N) Gross-Neveu model of Dirac fermions at large N and strong coupling using the Euclidean inversion formula. These models are considered in odd space time dimensions d and held at finite temperature and finite real chemical potential μ measured in units of the temperature. We show that these one point functions simplify both at large spin and large d. At large spin, the one point functions behave as though the theory is free, the chemical potential appears through a simple pre-factor which is either cosh μ or sinh μ depending on whether the spin is even or odd. At large d, but at finite spin and chemical potential, the 1-point functions are suppressed exponentially in d compared to the free theory. We study a fixed point of the critical Gross-Neveu model in d = 3 with 1-point functions exhibiting a branch cut in the chemical potential plane. The critical exponent for the free energy or the pressure at the branch point is 3/2 which coincides with the mean field exponent of the Lee-Yang edge singularity for repulsive core interactions.

Stationary Mean Field Games on networks with sticky transition conditions

We study stochastic Mean Field Games on networks with sticky transition conditions. In this setting, the diffusion process governing the agent's dynamics can spend finite time both in the interior of the edges and at the vertices. The corresponding generator is subject to limitations concerning second-order derivatives and the invariant measure breaks down into a combination of an absolutely continuous measure within the edges and a sum of Dirac measures positioned at the vertices. Additionally, the value function, solution to the Hamilton-Jacobi-Bellman equation, satisfies generalized Kirchhoff conditions at the vertices.

Stability of stationary states for mean field models with multichromatic interaction potentials

Abstract We consider weakly interacting diffusions on the torus, for multichromatic interaction potentials. We consider interaction potentials that are not $H$-stable, leading to phase transitions in the mean field limit. We show that the mean field dynamics can exhibit multipeak stationary states, where the number of peaks is related to the number of nonzero Fourier modes of the interaction. We also consider the effect of a confining potential on the structure of non-uniform steady states. We approach the problem by means of analysis, perturbation theory and numerical simulations for the interacting particle systems and the PDEs.

Anomalous U(1)A couplings and the Columbia plot

When the quark masses are lighter than those in QCD, the standard lore is that a chiral transition of first order must emerge for three light flavors. Recently, however, numerical simulations on the lattice suggest that the chiral transition is of second order in the chiral limit. Using an extended linear sigma model in the mean field approximation, we study the relation between terms which break the anomalous, U(1)A symmetry and the order of the chiral phase transition, especially how a chiral transition of second order can arise for three massless flavors. We note that in an (unphysical) region of the “Columbia” phase diagram, when the strange quark mass is light and negative, corresponding to topological angle θ=π, the CP symmetry is spontaneously broken. Published by the American Physical Society 2025

Universality of Mean-Field Antiferromagnetic Order in an Anisotropic 3D Hubbard Model at Half-Filling

We study Hartree–Fock theory at half-filling for the 3D anisotropic Hubbard model on a cubic lattice with hopping parameter t in the x- and y-directions and a possibly different hopping parameter tz in the z-direction; this model interpolates between the 2D and 3D Hubbard models corresponding to the limiting cases tz=0 and tz=t, respectively. We first derive all-order asymptotic expansions for the density of states. Using these expansions and units such that t=1, we analyze how the Néel temperature and the antiferromagnetic mean field depend on the coupling parameter, U, and on the hopping parameter tz. We derive asymptotic formulas valid in the weak coupling regime, and we study in particular the transition from the three-dimensional to the two-dimensional model as tz→0. It is found that the asymptotic formulas are qualitatively different for tz=0 (the two-dimensional case) and tz>0 0$$\\end{document}]]> (the case of nonzero hopping in the z-direction). Our results show that certain universality features of the three-dimensional Hubbard model are lost in the limit tz→0 in which the three-dimensional model reduces to the two-dimensional model.

Study of thermohydrodynamic processes in the air environment in the system of melting ice on the wires of the power transmission line

The paper considers issues related to modeling thermal and hydrodynamic processes in the "wire – ice shell – air" system that occur during melting of ice on wires. The problem of ice shell growth on the surface of power transmission line wires has been known for a long time, and many works in the field of ice growth control and technical means of combating this phenomenon are devoted to its solution. Recently, works have appeared on melting systems that operate without disconnecting lines from consumers, which increases the reliability and uninterruptible power supply, reduces economic losses from undersupply of products during power supply interruptions. The process of ice melting can occur under conditions of heating the conductors with a high current to a steady positive temperature until the ice shell is destroyed. In this case, switching to the melting mode is carried out for a short period of time. An alternative to this method is to combine power supply to consumers and ice melting. In this case, the heat generation capacity in the wires is less, the melting time is increased, but there is no need to disconnect consumers. The problem of maintaining the line in the operating mode of transmitting electric energy to consumers is solved by additionally loading the line with reactive currents by connecting a certain inductive load. The increase in currents and power coming from the supply transformer to the line must be technically feasible so as not to overload the source and not cause its shutdown. Due to power limitations, it is necessary to carry out accurate calculations of thermal processes to determine acceptable modes of melting the ice layer. Complex modeling of thermohydrodynamic processes in the "wire – ice shell – air" system is considered. Several methods for determining the coefficients of convective heat exchange at the boundaries of the conductor at different wind speeds are considered.

Quantum-Ordering Ambiguities in Weak Chern—Simons 4D Gravity and Metastability of the Condensate-Induced Inflation

In this work, we elaborate further on a (3+1)-dimensional cosmological Running-Vacuum-type-Model (RVM) of inflation based on string-inspired Chern-Simons(CS) gravity, involving axions coupled to gravitational-CS(gCS) anomalous terms. Inflation in such models is caused by primordial-gravitational-waves(GW)-induced condensation of the gCS terms, which leads to a linear-axion potential. We demonstrate that this inflationary phase may be metastable, due to the existence of imaginary parts of the gCS condensate. These are quantum effects, proportional to commutators of GW perturbations, hence vanishing in the classical theory. Their existence is quantum-ordering-scheme dependent. We argue in favor of a physical importance of such imaginary parts, which we compute to second order in the GW (tensor) perturbations in the framework of a gauge-fixed effective Lagrangian, within a (mean field) weak-quantum-gravity-path-integral approach. We thus provide estimates of the inflation lifetime. On matching our results with the inflationary phenomenology, we fix the quantum-ordering ambiguities, and obtain an order-of-magnitude constraint on the String-Mass-Scale-to-Planck-Mass ratio, consistent with previous estimates by the authors in the framework of a dynamical-system approach to linear-axion RVM inflation. Finally, we examine the role of periodic modulations in the axion potential induced by non-perturbative effects on the slow-roll inflationary parameters, and find compatibility with the cosmological data.

FragPT2: Multifragment Wave Function Embedding with Perturbative Interactions.

Embedding techniques allow the efficient description of correlations within localized fragments of large molecular systems while accounting for their environment at a lower level of theory. We introduce FragPT2: a novel embedding framework that addresses multiple interacting active fragments. Fragments are assigned separate active spaces, constructed by localizing canonical molecular orbitals. Each fragment is then solved with a multireference method, self-consistently embedded in the mean field from other fragments. Finally, interfragment correlations are reintroduced through multireference perturbation theory. Our framework provides an exhaustive classification of interfragment interaction terms, offering a tool to analyze the relative importance of various processes such as dispersion, charge transfer, and spin exchange. We benchmark FragPT2 on challenging test systems, including N2 dimers, multiple aromatic dimers, and butadiene. We demonstrate that our method can be successful even for fragments defined by cutting through a covalent bond.

Satellites reveal different stories of marine heatwaves in the sea-ice-covered pan-Arctic

Satellite observations provide valuable information on the rapidly increasing marine heatwaves over the Arctic Ocean, yet current assessments of these events lack reliability because the satellite-based temperature in ice-covered regions heavily relies on ice conditions. Here we compared the marine heatwaves derived from two commonly used satellite products to evaluate the potential influences of sea ice in the pan-Arctic. We found inconsistent behaviors of marine heatwaves in both mean fields and temporal variations on interannual and seasonal timescales using two datasets, which became even larger in recent years when they showed opposite tendencies over regions with higher ice concentrations (>50%). Our findings revealed our knowledge of marine heatwaves in the Arctic is facing challenges due to the large influences of sea ice and datasets that were ignored in previous studies, highlighting an urgent need for in situ observations and consistent and reliable long-time datasets for the warming Arctic.

A new log-weighted Trudinger-Moser inequality in $ \mathbb{R}^N,\ N \geq 2, $ and applications to some mean field equation

A new log-weighted Trudinger-Moser inequality in $ \mathbb{R}^N,\ N \geq 2, $ and applications to some mean field equation

Regularized Multi-Decoder Ensemble for an Error-Aware Scene Representation Network.

Feature grid Scene Representation Networks (SRNs) have been applied to scientific data as compact functional surrogates for analysis and visualization. As SRNs are black-box lossy data representations, assessing the prediction quality is critical for scientific visualization applications to ensure that scientists can trust the information being visualized. Currently, existing architectures do not support inference time reconstruction quality assessment, as coordinate-level errors cannot be evaluated in the absence of ground truth data. By employing the uncertain neural network architecture in feature grid SRNs, we obtain prediction variances during inference time to facilitate confidence-aware data reconstruction. Specifically, we propose a parameter-efficient multi-decoder SRN (MDSRN) architecture consisting of a shared feature grid with multiple lightweight multi-layer perceptron decoders. MDSRN can generate a set of plausible predictions for a given input coordinate to compute the mean as the prediction of the multi-decoder ensemble and the variance as a confidence score. The coordinate-level variance can be rendered along with the data to inform the reconstruction quality, or be integrated into uncertainty-aware volume visualization algorithms. To prevent the misalignment between the quantified variance and the prediction quality, we propose a novel variance regularization loss for ensemble learning that promotes the Regularized multi-decoder SRN (RMDSRN) to obtain a more reliable variance that correlates closely to the true model error. We comprehensively evaluate the quality of variance quantification and data reconstruction of Monte Carlo Dropout (MCD), Mean Field Variational Inference (MFVI), Deep Ensemble (DE), and Predicting Variance (PV) in comparison with our proposed MDSRN and RMDSRN applied to state-of-the-art feature grid SRNs across diverse scalar field datasets. We demonstrate that RMDSRN attains the most accurate data reconstruction and competitive variance-error correlation among uncertain SRNs under the same neural network parameter budgets. Furthermore, we present an adaptation of uncertainty-aware volume rendering and shed light on the potential of incorporating uncertain predictions in improving the quality of volume rendering for uncertain SRNs. Through ablation studies on the regularization strength and decoder count, we show that MDSRN and RMDSRN are expected to perform sufficiently well with a default configuration without requiring customized hyperparameter settings for different datasets.

Implementing the hardcore concept in the mean field of the Tamm-Dancoff approximation

Implementing the hardcore concept in the mean field of the Tamm-Dancoff approximation

Mean field decoupling of single impurity Anderson model through auxiliary Majorana fermions

Mean field decoupling of single impurity Anderson model through auxiliary Majorana fermions

Optimizing the identification of long-interval intracortical inhibition from the dorsolateral prefrontal cortex.

This study aimed to optimally evaluate the effect of the long-interval intracortical inhibition (LICI) in the dorsolateral prefrontal cortex (DLPFC) through transcranial magnetic stimulation combined with electroencephalography (TMS-EEG) by eliminating the volume conductance with signal source estimation and using a realistic sham coil as a control. We compared the LICI effects from the DLPFC between the active and sham stimulation conditions in 27 healthy participants. Evoked responses between the two conditions were evaluated at the sensor and source levels. At the sensor level, a significant LICI effect was confirmed in the active condition in the global mean field power analysis; however, in the local mean field power analysis focused on the DLPFC, no LICI effect was observed in the active condition. However, in the signal source estimation analysis for the DLPFC, we could reconfirm a significant LICI effect (p=0.023) in the interval 30-250ms post-stimulus, compared to the sham condition. Our results demonstrate that application of realistic sham stimulation condition and source estimation method allows for a robust and optimal identification of the LICI effect in the DLPFC. The optimal DLPFC-LICI effect was identified by the use of the sophisticated sham coil.

Approximation and perturbations of stable solutions to a stationary mean field game system

Approximation and perturbations of stable solutions to a stationary mean field game system

Joint Resource Allocation for UAV-Assisted V2X Communication With Mean Field Multi-Agent Reinforcement Learning

Joint Resource Allocation for UAV-Assisted V2X Communication With Mean Field Multi-Agent Reinforcement Learning

Small mass limit for stochastic N-interacting particles system in [formula omitted] in mean field limit

An L2(Rd)-valued stochastic N-interacting particles system with small mass is investigated. Mean field limit and the propagation of chaos are derived. Moreover the small mass limit of the solution is also built, which can be seen as a Smoluchowski–Kramers approximation on unbounded domain. Here a key step is the asymptotic compactness of the distribution of the solution, which is derived via a splitting technique of the domain Rd and some estimation of the solution for the mean field limit equation. We also show that the limits N→∞ and ϵ→0 commute.

Dark matter influence on quarkyonic stars: a relativistic mean field analysis

The formulation of quarkyonic matter consists of treating both quarks and nucleons as quasi-particles, where a cross-over transition occurs between the two phases. This work is based on some of the early ideas of quark matter (QM). It has satisfied the different observational constraints on the neutron star (NS), such as its maximum mass and the canonical radius. In addition, we put an extra component inside the NS, known as Dark Matter (DM) because it is trapped due to its immense gravitational potential. In this work, we explore the impact of fermionic DM on the structure of the NS. The equation of state (EOS) is derived for the NS with the quarkyonic matter by assuming that nucleons and quarks are in equilibrium, followed by the relativistic mean-field (RMF) formalism. The recently modeled two parameterizations, such as G3 and IOPB-I, are taken to calculate the various macroscopic properties of the NS. The three unknown parameters such as the transition density (nt ), the QCD confinement scale (Λcs), and the DM Fermi momentum (k f DM) are varied to obtain the NS properties. The quarkyonic matter stiffens the EOS while DM softens it. The mutual combination provides good theoretical descriptions for the magnitude of macroscopic properties consistent with the different observational results. Also, one can estimate the parameters of the DM admixed quarkyonic star with different statistical analyses, which can be further used to explore the other properties of the quarkyonic star.

Ciclo de maturação e relações entre grãos processados e frutos de café robustas amazônicos

ABSTRACT This study aimed to characterize the outturn index, field outturn index, uniformity of maturity, and maturation cycle of fifteen Coffea canephora genotypes grown in different environments of the Western Amazon. Conducted in Amazonas (Itacoatiara and Manaus) and Rondônia (Porto Velho), the research evaluated the performance of ten cultivars and five promising genotypes from Embrapa. The genotype × environment interaction was significant, indicating different performance of clones across environments. Genotypic coefficients surpassed environmental ones, indicating a genetic influence on outturn indices and uniformity of maturity. The mean outturn index was 24.68%, and the field outturn index was 22.57%, with Itacoatiara having the highest mean values. The overall mean fruit uniformity of maturity was 63.02%, with Porto Velho achieving the highest mean uniformity value (71.78%). The cultivar BRS1216 exhibited the best performance for outturn indices and provided the highest gain from selection across environments, showing wide adaptability for the outturn index and adaptability to environments favorable for field outturn. Cultivars BRS3210 and BRS3220 achieved more than 82% uniformity of maturity across locations, with BRS3210 adapting to favorable environments and BRS3220 adapting to unfavorable ones. Additionally, BRS3220 had a high mean field outturn index, indicating wide adaptability and high phenotypic stability. The evaluated Amazon Robusta clones and cultivars displayed the expected maturation cycles.

Kaons and antikaons in isospin asymmetric dense resonance matter at finite temperature

We study the in-medium properties of kaons and antikaons in isospin asymmetric hot and dense resonance matter within the chiral SU(3) hadronic mean field model. Along with nucleons and hyperons, the interactions of K and K¯ mesons with all decuplet baryons (Δ++,+,0,−,Σ*±,0,Ξ*0,−,Ω−) are explicitly considered in the dispersion relations. The properties of mesons in the chiral SU(3) model are modified at finite density and temperature of asymmetric resonance matter through the exchange of scalar fields σ, ζ, and δ and the vector fields ω, ρ, and ϕ. The presence of resonance baryons in the medium at finite temperature is observed to modify significantly the effective masses of K and K¯ mesons. We also calculated the optical potentials of kaons and antikaons as a function of momentum in resonance matter. The present study of in-medium masses and optical potentials of kaons and antikaons will be important for understanding the experimental observables from the heavy-ion collision experiments where hot and dense matter may be produced. Our results indicate that when resonance baryons are present within the medium at finite baryonic density, the mass reduction of kaons and antikaons becomes more pronounced as the temperature of the medium increases from zero to 100 and 150 MeV. The study of the optical potentials of kaons and antikaons reveals a stronger correlation with strangeness fraction compared to isospin asymmetry. Published by the American Physical Society 2024