Universality and self-similarity of an energy-constrained sandpile model with random neighbors

We study an energy-constrained sandpile model with random neighbors. The critical behavior of the model is in the same universality class as the mean-field self-organized criticality sandpile. The critical energy E-c depends on the number of neighbors n for each site, but the various exponents are independent of n. A self-similar structure with n-1 major peaks is developed for the energy distribution p(E) when the system approaches its stationary state. The avalanche dynamics contributes to the major peaks appearing at E-Pk = 2k/(2n - 1) with k = 1,2,...,n-1, while the fine self-similar structure is a natural result of the way the system is disturbed. [S1063-651X(99)10307-6].

ON THE UNIVERSALITY OF 2-DIMENSIONAL DIFFUSION-LIMITED DEPOSITION

A history dependent stick probability is introduced to the diffusion-limited deposition model. The exponents in the scaling laws are calculated. The universality class is also discussed.

Random neighbor sandpile model with constrained total energy

We propose as energy-constrained sandpile model with random neighbors. The critical behavior of the model is in the same universality class as the mean-field self-organized criticality sandpile. The critical energy E-c depends on the number of neighbors n of each site, but the various exponents do not. For n = 6, we got that E-c = 0.4545; and a self-similar structure of the energy distribution function with five major peaks is also observed. This is a natural result of system dynamics and the way the system is disturbed.

Disorder-induced phase transition in a one-dimensional model of rice pile

We propose a one-dimensional rice-pile model which connects the 1D BTW sandpile model (Phys. Rev. A 38 (1988) 364) and the Oslo rice-pile model (Phys. Rev. Lett. 77 (1997) 107) in a continuous manner. We found that for a sufficiently large system, there is a sharp transition between the trivial critical behaviour of the 1D BTW model and the self-organized critical (SOC) behaviour. When there is SOC, the model belongs to a known universality class with the avalanche exponent tau = 1.53. (C) 1999 Elsevier Science B.V. All rights reserved.

Global quantum correlations in finite-size spin chains

We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord, we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.

Full characterization of the quantum linear-zigzag transition in atomic chains

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. Based on the emergent symmetry Z2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. An extensive Density Matrix Renormalization Group analysis is performed, resulting in an high-precision evaluation of the critical exponents and of the central charge of the system, confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. Quantum corrections to the classical phase diagram are computed, and the range of experimental parameters where quantum effects play a role is provided. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.

CRITICAL PROCESSES, LANGEVIN EQUATION AND UNIVERSALITY

In nature there are ubiquitous systems that can naturally approach critical states, The Langevin equation in the discrete version can be used to describe a class of critical processes, which are characterized by power-law behaviors and scaling relations. As an example, we present a simple model for a clinical thermometer, whose reading cannot fall even when its temperature decreases. The fibers bundle model and the spring-block model are also shown to belong to such a class.

The Effects of Social Class and Ethnicity on Gender Differences in GCSE Attainment: A Secondary Analysis of the Youth Cohort Study of England and Wales 1997-2001

This article is based upon a secondary analysis of the Youth Cohort Study of England and Wales 1998 and examines the effects of social class and ethnicity on gender differences in GCSE attainment for those who left school in 1997 (n = 14,662). The article shows that both social class and ethnicity exert a far greater influence on the GCSE performance of boys and girls than gender. Moreover, the article also shows that an interaction effect is present between social class and gender and also between ethnicity and gender in relation to their impact upon GCSE attainment. More specifically, the findings suggest that a strong correlation exists such that the lower the overall levels of educational attainment for any group (whether that group is defined in terms of social class or ethnicity), the higher the gender differences that exist between those within that group.

Symbolic violence and the neighbourhood: young working class girls' attitudes to education in Belfast

This article focuses on the experiences of 7-8 year old working-class girls in Belfast, Northern Ireland and their attitudes towards education. It shows how their emerging identities tend to emphasize relationships, marriage and motherhood at the expense of a concern with education and future careers. The article suggests that one important factor that can help explain this is the influence of the local neighbourhood. In drawing upon Bourdieu's concepts of symbolic violence and habitus and Elias' notion of figuration, the article shows how the local neighbourhood represents the parameters of the girls' social worlds. It provides the context within which the girls tend to focus on social relations within their community and particularly on family relationships, marriage and children. It also provides the context within which the girls tend to develop strong interdependent relationships with their mothers that also tend to encourage and reinforce the girls' particular gendered identities. The article concludes by arguing that there is a need for more research on working-class girls and education to look beyond the school to incorporate, more fully, an understanding of the influence of the family and local neighbourhood on their attitudes towards education and their future career aspirations.