Monte Carlo simulations of the three-dimensional XY spin glass focusing on the chiral and the spin order

The ordering of the three-dimensional isotropic {\it XY} spin glass with the nearest-neighbor random Gaussian coupling is studied by extensive Monte Carlo simulations. To investigate the ordering of the spin and the chirality, we compute several independent physical quantities including the glass order parameter, the Binder parameter, the correlation-length ratio, the overlap distribution and the non-self-averageness parameter, {\it etc}, for both the spin-glass (SG) and the chiral-glass (CG) degrees of freedom. Evidence of the spin-chirality decoupling, {\it i.e.}, the CG and the SG order occurring at two separated temperatures, $0<T_{SG}<T_{CG}$, is obtained from the glass order parameter, which is fully corroborated by the Binder parameter. By contrast, the CG correlation-length ratio yields a rather pathological and inconsistent result in the range of sizes we studied, which may originate from the finite-size effect associated with a significant short-length drop-off of the spatial CG correlations. Finite-size-scaling analysis yields the CG exponents $\nu_{CG}=1.36^{+0.15}_{-0.37}$ and $\eta_{CG}=0.26^{+0.29}_{-0.26}$, and the SG exponents $\nu_{SG}=1.22^{+0.26}_{-0.06}$ and $\eta_{SG}=-0.54^{+0.24}_{-0.52}$. The obtained exponents are close to those of the Heisenberg SG, but are largely different from those of the Ising SG. The chiral overlap distribution and the chiral Binder parameter exhibit the feature of a continuous one-step replica-symmetry breaking (1RSB), consistently with the previous reports. Such a 1RSB feature is again in common with that of the Heisenberg SG, but is different from the Ising one, which may be the cause of the difference in the CG critical properties from the Ising SG ones despite of a common $Z_2$ symmetry.Comment: 15 pages, 31 figure

Dynamical Singularities of Glassy Systems in a Quantum Quench

We present a prototype of behavior of glassy systems driven by quantum dynamics in a quenching protocol by analyzing the random energy model in a transverse field. We calculate several types of dynamical quantum amplitude and find a freezing transition at some critical time. The behavior is understood by the partition-function zeros in the complex temperature plane. We discuss the properties of the freezing phase as a dynamical chaotic phase, which are contrasted to those of the spin-glass phase in the static system.Comment: 6 pages, 5 figure

Partition-function zeros of spherical spin glasses and their relevance to chaos

We investigate partition-function zeros of the many-body interacting spherical spin glass, the so-called $p$-spin spherical model, with respect to the complex temperature in the thermodynamic limit. We use the replica method and extend the procedure of the replica symmetry breaking ansatz to be applicable in the complex-parameter case. We derive the phase diagrams in the complex-temperature plane and calculate the density of zeros in each phase. Near the imaginary axis away from the origin, there is a replica symmetric phase having a large density. On the other hand, we observe no density in the spin-glass phases, irrespective of the replica symmetry breaking. We speculate that this suggests the absence of the temperature chaos. To confirm this, we investigate the multiple many-body interacting case which is known to exhibit the chaos effect. The result shows that the density of zeros actually takes finite values in the spin-glass phase, even on the real axis. These observations indicate that the density of zeros is more closely connected to the chaos effect than the replica symmetry breaking.Comment: 22 pages, 8 figure

Approximate cross-validation formula for Bayesian linear regression

Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set. Despite its wide applicability, the rather heavy computational cost can prevent its use as the system size grows. To resolve this difficulty in the case of Bayesian linear regression, we develop a formula for evaluating the leave-one-out CV error approximately without actually performing CV. The usefulness of the developed formula is tested by statistical mechanical analysis for a synthetic model. This is confirmed by application to a real-world supernova data set as well.Comment: 5 pages, 2 figures, invited paper for Allerton2016 conferenc

Replica symmetry breaking, complexity and spin representation in the generalized random energy model

We study the random energy model with a hierarchical structure known as the generalized random energy model (GREM). In contrast to the original analysis by the microcanonical ensemble formalism, we investigate the GREM by the canonical ensemble formalism in conjunction with the replica method. In this analysis, spin-glass-order parameters are defined for respective hierarchy level, and all possible patterns of replica symmetry breaking (RSB) are taken into account. As a result, we find that the higher step RSB ansatz is useful for describing spin-glass phases in this system. For investigating the nature of the higher step RSB, we generalize the notion of complexity developed for the one-step RSB to the higher step and demonstrate how the GREM is characterized by the generalized complexity. In addition, we propose a novel mean-field spin-glass model with a hierarchical structure, which is equivalent to the GREM at a certain limit. We also show that the same hierarchical structure can be implemented to other mean-field spin models than the GREM. Such models with hierarchy exhibit phase transitions of multiple steps in common.Comment: 30 pages, 11 figures; minor change

Adolescents and Young Adults in Latin America, Critical Decisions at a Critical Age: Young Adult Labor Market Experience

This study explores and analyzes the labor market experience of young adults in 18 Latin American countries. For men, the period of young adulthood (18-25 years of age) was found to be one of smooth convergence towards patterns associated with full adulthood. Females show more complex and less clear-cut trajectories, which seem to be affected by entrance into motherhood. Educational attainment shapes the labor market experience of young adults, regardless of gender: the more educated postpone entry into the market, and more educated women display higher participation rates as they reach late young adulthood. Also, during young adulthood, the more educated display higher unemployment rates, possibly because they are newer in the market, but their rate of participation in the informal sector of the economy is lower. Female labor market experience was found to be affected by motherhood. In many countries women with lower levels of education leave the labor market during young adulthood, while women with higher levels of education postpone such exits and are also less likely to leave. Finally, young Latin American adults with college education were found to experience rapid labor market absorption, featuring swift entry into the formal sector, high participation rates and low and rapidly decreasing unemployment rates. Earnings equations show that education, experience and gender have significant and positive effects on the earnings of young adults. In general, returns from education increase with age and educational level, with the sharpest marginal change occurring in early young adulthood. Return for education and experience of young adults tend to be close to those obtained by prime age adults, although in the case of experience the returns obtained by young adults tend to be larger. In general, formal education has a consistently larger effect than experience. Although the previous findings hold for young adults in almost all countries included in the study, it is important to note that the individual countries results show large variation in the levels of all coefficients (education, experience and gender) and among age groups.