Found 1683 results, showing the newest relevant preprints. Sort by relevancy only.Update me on new preprints

Mean-**field** phase diagram and spin glass phase of the dipolar Kagome
Ising antiferromagnet

Moreover, they allow us to interpret the dynamical slowing down observed in the work of Hamp & al. as a remnant of a spin glass transition taking place at the

**mean**-**field**level (and expected to be avoided in 2 dimensions). Expand abstract. We derive the equilibrium phase diagram of the classical dipolar Ising antiferromagnet at the

**mean**-**field**level on a geometry that mimics the two dimensional Kagome lattice. Our**mean**-**field**treatment is based on the combination of the cluster variational Bethe-Peierls formalism and the cavity method, developed in the context of the glass transition, and is complementary to the Monte Carlo simulations realized in [Phys. Rev. B 98, 144439 (2018)]. Our results confirm the nature of the low temperature crystalline phase which is reached through a weakly first-order phase transition. Moreover, they allow us to interpret the dynamical slowing down observed in the work of Hamp & al. as a remnant of a spin glass transition taking place at the**mean**-**field**level (and expected to be avoided in 2 dimensions).150 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

Spectral gap in $\mathcal O(n)$-model and chain of oscillators using Schr\"odinger operators

We study the dependence of the spectral gap for the generator of the continuous-time Glauber dynamics for all $\mathcal O(n)$-models with mean-field interaction and magnetic field, below the critical temperature on the number $N$ of particles. Expand abstract.

We study the dependence of the spectral gap for the generator of the continuous-time Glauber dynamics for all $\mathcal O(n)$-models with

**mean**-**field**interaction and magnetic field, below the critical temperature on the number $N$ of particles. We also analyze the behaviour of the spectral gap for a classical heat conduction model, the so-called Chain of oscillators for various configurations in terms of the number of particles. In both cases, we reduce the analysis of the entirely classical models to the study of Schr\"odinger operators.151 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Implications of the fermion vacuum term in the extended SU(3) Quark Meson model on compact stars properties

We study the impact of the fermion vacuum term in the SU(3) quark meson model on the equation of state and determine the vacuum parameters for various sigma meson masses. Expand abstract.

We study the impact of the fermion vacuum term in the SU(3) quark meson model on the equation of state and determine the vacuum parameters for various sigma meson masses. We examine its influence on the equation of state and on the resulting mass radius relations for compact stars. The tidal deformability $\Lambda$ of the stars is studied and compared to the results of the

**mean****field**approximation. Parameter sets which fulfill the tidal deformability bounds of GW170817 together with the observed two solar mass limit turn out to be restricted to a quite small parameter range in the**mean****field**approximation. The extended version of the model does not yield solutions fulfilling both constraints. Furthermore, no first order chiral phase transition is found in the extended version of the model, not allowing for the twin star solutions found in the**mean****field**approximation.151 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv

Critical properties of the Ising model in hyperbolic space

In contrast to recent

**field**theory calculations, which predict a non-mean-field fixed point for the ferromagnetic-paramagnetic phase-transition of the Ising model on three-dimensional hyperbolic space, our computations reveal a**mean**-field behavior. Expand abstract. The Ising model exhibits qualitatively different properties in hyperbolic space in comparison to its flat space counterpart. Due to the negative curvature, a finite fraction of the total number of spins reside at the boundary of a volume in hyperbolic space. As a result, boundary conditions play an important role even when taking the thermodynamic limit. We investigate the bulk thermodynamic properties of the Ising model in two and three dimensional hyperbolic spaces using Monte Carlo and high and low-temperature series expansion techniques. To extract the true bulk properties of the model in the Monte Carlo computations, we consider the Ising model in hyperbolic space with periodic boundary conditions. We compute the critical exponents and critical temperatures for different tilings of the hyperbolic plane and show that the results are of

**mean**-**field**nature. We compare our results to the 'asymptotic' limit of tilings of the hyperbolic plane: the Bethe lattice, explaining the relationship between the critical properties of the Ising model on Bethe and hyperbolic lattices. Finally, we analyze the Ising model on three dimensional hyperbolic space using Monte Carlo and high-temperature series expansion. In contrast to recent**field**theory calculations, which predict a non-mean-**field**fixed point for the ferromagnetic-paramagnetic phase-transition of the Ising model on three-dimensional hyperbolic space, our computations reveal a**mean**-**field**behavior.151 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

**Mean** **Field** approach to stochastic control with partial information

Indeed,

**Mean****Field**Control Theory leads to very complex equations, like the Master equation, which is a nonlinear infinite dimensional P. Expand abstract. The classical stochastic control problem under partial information can be formulated as a control problem for Zakai equation, whose solution is the unnormalized conditional probability distribution of the state of the system. Zakai equation is a stochastic Fokker-Planck equation. Therefore, the problem to be solved is similar to that met in

**Mean****Field**Control theory. Since**Mean****Field**Control theory is much posterior to the development of Stochastic Control with partial information, the tools, techniques, and concepts obtained in the last decade, for**Mean****Field**Games and**Mean****field**type Control theory, have not been used for the control of Zakai equation. Our objective is to connect the two theories. We get the power of new tools, and we get new insights for the problem of stochastic control with partial information. For**mean****field**theory, we get new interesting applications, but also new problems. Indeed,**Mean****Field**Control Theory leads to very complex equations, like the Master equation, which is a nonlinear infinite dimensional P.D.E., for which general theorems are hardly available, although active research in this direction is performed. Direct methods are useful to obtain regularity results. We will develop in detail the LQ regulator problem, but since we cannot just consider the Gaussian case, well-known results, such as the separation principle is not available. An important result is available in the literature, due to A. Makowsky. It describes the solution of Zakai equation for linear systems with general initial condition (non-gaussian). We show that the separation principle can be extended for quadratic pay-off functionals, but the Kalman filter is much more complex than in the gaussian case. Finally we compare our work to the work of E. Bandini et al. and we show that the example E. Bandini et al. provided does not cover ours. Our system remains nonlinear in their setting.154 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

On a **Mean** **Field** Optimal Control Problem

We notice this model is in close connection with the theory of

**mean**-**field**games systems. Expand abstract. In this paper we consider a

**mean****field**optimal control problem with an aggregation-diffusion constraint, where agents interact through a potential, in the presence of a Gaussian noise term. Our analysis focuses on a PDE system coupling a Hamilton-Jacobi and a Fokker-Planck equation, describing the optimal control aspect of the problem and the evolution of the population of agents, respectively. The main contribution of the paper is a result on the existence of solutions for the aforementioned system. We notice this model is in close connection with the theory of**mean**-**field**games systems. However, a distinctive feature concerns the nonlocal character of the interaction; it affects the drift term in the Fokker-Planck equation as well as the Hamiltonian of the system, leading to new difficulties to be addressed.154 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

A quartet bcs-like theory

We introduce a BCS-like theory for the quartet correlations induced by the isovector pairing interaction. Expand abstract.

We introduce a BCS-like theory for the quartet correlations induced by the isovector pairing interaction. It is based on a coherent state of BCS type and, unlike usual

**mean****field**approaches, it displays a vanishing pair anomalous density $\langle c^\dagger c^\dagger\rangle =0$. We find good agreement between our theory and the exact results. We discuss how the pairing and quarteting correlations share some similar qualitative features within the BCS approach. However, there is no sharp quarteting phase transition. We also present various ways in which our theory may be further developed.154 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

A discretized version of Krylov's estimate and its applications

Moreover, we also show the propagation of chaos for Euler's approximation of

**mean**-**field**SDEs. Expand abstract. In this paper we prove a discretized version of Krylov's estimate for discretized It\^o's processes. As applications, we study the weak and strong convergences for Euler's approximation of

**mean**-**field**SDEs with measurable discontinuous and linear growth coefficients. Moreover, we also show the propagation of chaos for Euler's approximation of**mean**-**field**SDEs.155 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Intrinsic Cluster-Shaped Density Waves in Cellular Dynamical **Mean**-Field
Theory

We discuss the limitations of periodization regarding this phenomenon, and we present

**mean**-**field**density-wave models that reproduce CDMFT results at low energy in the superconducting state. Expand abstract. It is well known that cellular dynamical

**mean**-**field**theory (CDMFT) leads to the artificial breaking of translation invariance. In spite of this, it is one of the most successful methods to treat strongly correlated electrons systems. Here, we investigate in more detail how this broken translation invariance manifests itself. This allows to disentangle artificial broken translation invariance effects from the genuine strongly correlated effects captured by CDMFT. We report artificial density waves taking the shape of the cluster---cluster density waves---in all our zero temperature CDMFT solutions, including pair density waves in the superconducting state. We discuss the limitations of periodization regarding this phenomenon, and we present**mean**-**field**density-wave models that reproduce CDMFT results at low energy in the superconducting state. We then discuss how these artificial density waves help the agreement of CDMFT with high temperature superconducting cuprates regarding the low-energy spectrum, in particular for subgap structures observed in tunnelling microscopy. We relate these subgap structures to nodal and anti-nodal gaps in our results, similar to those observed in photoemission experiments. This fortuitous agreement suggests that spatial inhomogeneity may be a key ingredient to explain some features of the low-energy underdoped spectrum of cuprates with strongly correlated methods. This work deepens our understanding of CDMFT and clearly identifies signatures of broken translation invariance in the presence of strong correlations.155 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

Enhanced adiabatic index for hot neutron-rich matter from microscopic nuclear forces

We investigate the adiabatic index $\Gamma_{\mathrm{th}}$ of hot and dense nuclear matter from chiral effective field theory and find that the results are systematically larger than from typical mean field models. Expand abstract.

We investigate the adiabatic index $\Gamma_{\mathrm{th}}$ of hot and dense nuclear matter from chiral effective

**field**theory and find that the results are systematically larger than from typical**mean****field**models. We start by constructing the finite-temperature equation of state from chiral two- and three-nucleon forces, which we then use to fit a class of extended Skyrme energy density functionals. This allows for modeling the thermal index across the full range of densities and temperatures that may be probed in simulations of core-collapse supernovae and neutron star mergers, including the low-density inhomogeneous mixed phase. For uniform matter we compare the results to analytical expressions for $\Gamma_{\mathrm{th}}$ based on Fermi liquid theory. The correlation between the thermal index and the effective masses at nuclear saturation density is studied systematically through Bayesian modeling of the nuclear equation of state. We then study the behavior of $\Gamma_{\mathrm{th}}$ in both relativistic and non-relativistic**mean****field**models used in the astrophysical simulation community to complement those based on chiral effective**field**theory constraints from our own study. We derive compact parameterization formulas for $\Gamma_{\mathrm{th}}$ across the range of densities and temperatures encountered in core collapse supernovae and binary neutron star mergers, which we suggest may be useful for the numerical simulation community.158 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv