Magnetic incommensurability and fluctuating charge density waves in the repulsive Hubbard model

Magnetic and charge susceptibilities of the two-dimensional repulsive Hubbard model are investigated applying a strong coupling diagram technique in which the expansion in powers of the hopping constants is used. For small lattices and high temperatures results are in agreement with Monte Carlo simulations. With the departure from half-filling $x$ the low-frequency magnetic susceptibility becomes incommensurate and the incommensurability parameter grows with $x$. The incommensurability, its dependence on frequency and on $x$ resemble experimental results in lanthanum cuprates. Also for finite $x$ sharp maxima appear in the static charge susceptibility. The maxima are finite which points to the absence of the long-range charge ordering (static stripes). However, for $x\approx 0.12$ the maxima are located near the momenta $(0,\pm\pi/2)$, $(\pm\pi/2,0)$. In this case an interaction of carriers with tetragonal distortions can stabilize stripes with the wavelength of four lattice spacings, as observed in the low-temperature tetragonal phase of cuprates. As follows from the obtained results, the magnetic incommensurability is not a consequence of the stripes.Comment: 4 pages, 3 figures, manuscript for proceefings of LT2

What the brain 'Likes': neural correlates of providing feedback on social media.

Evidence increasingly suggests that neural structures that respond to primary and secondary rewards are also implicated in the processing of social rewards. The 'Like'-a popular feature on social media-shares features with both monetary and social rewards as a means of feedback that shapes reinforcement learning. Despite the ubiquity of the Like, little is known about the neural correlates of providing this feedback to others. In this study, we mapped the neural correlates of providing Likes to others on social media. Fifty-eight adolescents and young adults completed a task in the MRI scanner designed to mimic the social photo-sharing app Instagram. We examined neural responses when participants provided positive feedback to others. The experience of providing Likes to others on social media related to activation in brain circuity implicated in reward, including the striatum and ventral tegmental area, regions also implicated in the experience of receiving Likes from others. Providing Likes was also associated with activation in brain regions involved in salience processing and executive function. We discuss the implications of these findings for our understanding of the neural processing of social rewards, as well as the neural processes underlying social media use