On the Use of Optimized Monte Carlo Methods for Studying Spin Glasses

We start from recently published numerical data by Hatano and Gubernatis cond-mat/0008115 to discuss properties of convergence to equilibrium of optimized Monte Carlo methods (bivariate multi canonical and parallel tempering). We show that these data are not thermalized, and they lead to an erroneous physical picture. We shed some light on why the bivariate multi canonical Monte Carlo method can fail.Comment: 6 pages, 5 eps figures include

On the approach to equilibrium of an Hamiltonian chain of anharmonic oscillators

In this note we study the approach to equilibrium of a chain of anharmonic oscillators. We find indications that a sufficiently large system always relaxes to the usual equilibrium distribution. There is no sign of an ergodicity threshold. The time however to arrive to equilibrium diverges when $g \to 0$, $g$ being the anharmonicity.Comment: 8 pages, 5 figure

4D Spin Glasses in Magnetic Field Have a Mean Field like Phase

By using numerical simulations we show that the 4D $J=\pm 1$ Edwards Anderson spin glass in magnetic field undergoes a mean field like phase transition. We use a dynamical approach: we simulate large lattices (of volume $V$) and work out the behavior of the system in limit where both $t$ and $V$ go to infinity, but where the limit $V \to \infty$ is taken first. By showing that the dynamic overlap $q$ converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with the ones obtained by mean field computations.Comment: Physrev format, 5 ps figures include

Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses

We compute numerically small window overlaps in the three dimensional Edwards Anderson spin glass. We show that they behave in the way implied by the Replica Symmetry Breaking Ansatz, that they do not qualitatively differ from the full volume overlap and do not tend to a trivial function when increasing the lattice volume. On the contrary we show they are affected by small finite volume effects, and are interesting tools for the study of the features of the spin glass phase.Comment: 9 pages plus 5 figure

Understanding singularities in Cartan's and NSF geometric structures

In this work we establish a relationship between Cartan's geometric approach to third order ODEs and the 3-dim Null Surface Formulation (NSF). We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms.Comment: 22 pages, 2 figure

A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model

In this paper we study the fluctuations of the probability distributions of the overlap in mean field spin glasses in the presence of a magnetic field on the De Almeida-Thouless line. We find that there is a large tail in the left part of the distribution that is dominated by the contributions of rare samples. Different techniques are used to examine the data and to stress on different aspects of the contribution of rare samples.Comment: 13 pages, 11 figure

Equilibrium and off-equilibrium simulations of the 4d Gaussian spin glass

In this paper we study the on and off-equilibrium properties of the four dimensional Gaussian spin glass. In the static case we determine with more precision that in previous simulations both the critical temperature as well as the critical exponents. In the off-equilibrium case we settle the general form of the autocorrelation function, and show that is possible to obtain dynamically, for the first time, a value for the order parameter.Comment: 16 pages and 13 figures, uses epsfig.sty and rotate.sty. Some minor grammatical changes. Also available at http://chimera.roma1.infn.it/index_papers_complex.htm

Family well-being during the COVID-19 lockdown in Italy: Gender differences and solidarity networks of care

During the COVID-19 pandemic, families experienced new challenges related to reorganizing living spaces and the need to renegotiate domestic and care roles. This paper aims to understand how Italian families have reacted to this situation with respect to psychological well-being, the management of domestic and care activities and solidarity networks of care. The participants were 560 Italian subjects who reported having a parental role. The protocol included a measure of well-being (the General Health Questionnaire-12) and some questions related to the time dedicated to domestic activities or to caring for people, the perception of conflict within the family and solidarity networks of care. The data underline how mothers continued to devote more time to home and care activities than fathers, despite the presence of both partners at home during the lockdown. The results also indicate that mothers participated to a greater extent than fathers in solidarity activities, confirming that this dimension is linked to gender. Furthermore, fathers and mothers perceived a lower condition of well-being in relation to the pre-pandemic period

An approach to NLO QCD analysis of the semi-inclusive DIS data with modified Jacobi polynomial expansion method

It is proposed the modification of the Jacobi polynomial expansion method (MJEM) which is based on the application of the truncated moments instead of the full ones. This allows to reconstruct with a high precision the local quark helicity distributions even for the narrow accessible for measurement Bjorken $x$ region using as an input only four first moments extracted from the data in NLO QCD. It is also proposed the variational (extrapolation) procedure allowing to reconstruct the distributions outside the accessible Bjorken $x$ region using the distributions obtained with MJEM in the accessible region. The numerical calculations encourage one that the proposed variational (extrapolation) procedure could be applied to estimate the full first (especially important) quark moments

On the Phase Structure of the 3D Edwards Anderson Spin Glass

We characterize numerically the properties of the phase transition of the three dimensional Ising spin glass with Gaussian couplings and of the low temperature phase. We compute critical exponents on large lattices. We study in detail the overlap probability distribution and the equilibrium overlap-overlap correlation functions. We find a clear agreement with off-equilibrium results from previous work. These results strongly support the existence of a continuous spontaneous replica symmetry breaking in three dimensional spin glasses.Comment: 30 pages and 17 figures. Final version to be published in PR