Critical thermodynamics of three-dimensional chiral model for N > 3

The critical behavior of the three-dimensional $N$-vector chiral model is studied for arbitrary $N$. The known six-loop renormalization-group (RG) expansions are resummed using the Borel transformation combined with the conformal mapping and Pad\'e approximant techniques. Analyzing the fixed point location and the structure of RG flows, it is found that two marginal values of $N$ exist which separate domains of continuous chiral phase transitions $N > N_{c1}$ and $N N > N_{c2}$ where such transitions are first-order. Our calculations yield $N_{c1} = 6.4(4)$ and $N_{c2} = 5.7(3)$. For $N > N_{c1}$ the structure of RG flows is identical to that given by the $\epsilon$ and 1/N expansions with the chiral fixed point being a stable node. For $N < N_{c2}$ the chiral fixed point turns out to be a focus having no generic relation to the stable fixed point seen at small $\epsilon$ and large $N$. In this domain, containing the physical values $N = 2$ and $N = 3$, phase trajectories approach the fixed point in a spiral-like manner giving rise to unusual crossover regimes which may imitate varying (scattered) critical exponents seen in numerous physical and computer experiments.Comment: 12 pages, 3 figure

Progress in sensorimotor neuroscience of schizophrenia spectrum disorders: Lessons learned and future directions

The number of neuroimaging studies on movement disorders, sensorimotor, and psychomotor functioning in schizophrenia spectrum disorders (SSD) has steadily increased over the last two decades. Accelerated by the addition of the \u201csensorimotor domain\u201d to the Research Domain Criteria (RDoC) framework in January 2019, neuroscience research on the role of sensorimotor dysfunction in SSD has gained greater scientific and clinical relevance. To draw attention to recent rapid progress in the field, we performed a triennial systematic review (PubMed search from January 1st, 2018 through December 31st, 2020), in which we highlight recent neuroimaging findings and discuss methodological pitfalls as well as challenges for future research. The identified magnetic resonance imaging (MRI) studies suggest that sensorimotor abnormalities in SSD are related to cerebello-thalamo-cortico-cerebellar network dysfunction. Longitudinal and interventional studies highlight the translational potential of the sensorimotor domain as putative biomarkers for treatment response and as targets for non-invasive neurostimulation techniques in SSD