The 2D XY model on a finite lattice with structural disorder: quasi-long-range ordering under realistic conditions

We present an analytic approach to study concurrent influence of quenched non-magnetic site-dilution and finiteness of the lattice on the 2D XY model. Two significant deeply connected features of this spin model are: a special type of ordering (quasi-long-range order) below a certain temperature and a size-dependent mean value of magnetisation in the low-temperature phase that goes to zero (according to the Mermin-Wagner-Hohenberg theorem) in the thermodynamic limit. We focus our attention on the asymptotic behaviour of the spin-spin correlation function and the probability distribution of magnetisation. The analytic approach is based on the spin-wave approximation valid for the low-temperature regime and an expansion in the parameters which characterise the deviation from completely homogeneous configuration of impurities. We further support the analytic considerations by Monte Carlo simulations performed for different concentrations of impurities and compare analytic and MC results. We present as the main quantitative result of the work the exponent of the spin-spin correlation function power law decay. It is non universal depending not only on temperature as in the pure model but also on concentration of magnetic sites. This exponent characterises also the vanishing of magnetisation with increasing lattice size.Comment: 13 pages, 7 eps figures, style files include

Social Cognitive Networks and Social Cognitive Performance Across Individuals With Schizophrenia Spectrum Disorders and Healthy Control Participants

BACKGROUND: Schizophrenia spectrum disorders (SSDs) feature social cognitive deficits, although their neural basis remains unclear. Social cognitive performance may relate to neural circuit activation patterns more than to diagnosis, which would have important prognostic and therapeutic implications. The current study aimed to determine how functional connectivity within and between social cognitive networks relates to social cognitive performance across individuals with SSDs and healthy control participants. METHODS: Participants with SSDs (n = 164) and healthy control participants (n = 117) completed the Empathic Accuracy task during functional magnetic resonance imaging as well as lower-level (e.g., emotion recognition) and higher-level (e.g., theory of mind) social cognitive measures outside the scanner. Functional connectivity during the Empathic Accuracy task was analyzed using background connectivity and graph theory. Data-driven social cognitive networks were identified across participants. Regression analyses were used to examine network connectivity-performance relationships across individuals. Positive and negative within- and between-network connectivity strengths were also compared in poor versus good social cognitive performers and in SSD versus control groups. RESULTS: Three social cognitive networks were identified: motor resonance, affect sharing, and mentalizing. Regression and group-based analyses demonstrated reduced between-network negative connectivity, or segregation, and greater within- and between-network positive connectivity in worse social cognitive performers. There were no significant effects of diagnostic group on within- or between-network connectivity. CONCLUSIONS: These findings suggest that the neural circuitry of social cognitive performance may exist dimensionally. Across participants, better social cognitive performance was associated with greater segregation between social cognitive networks, whereas poor versus good performers may compensate via hyperconnectivity within and between social cognitive networks