Fisher's scaling relation above the upper critical dimension

Fisher's fluctuation-response relation is one of four famous scaling formulae and is consistent with a vanishing correlation-function anomalous dimension above the upper critical dimension d_c. However, it has long been known that numerical simulations deliver a negative value for the anomalous dimension there. Here, the apparent discrepancy is attributed to a distinction between the system-length and correlation- or characteristic-length scales. On the latter scale, the anomalous dimension indeed vanishes above d_c and Fisher's relation holds in its standard form. However, on the scale of the system length, the anomalous dimension is negative and Fisher's relation requires modification. Similar investigations at the upper critical dimension, where dangerous irrelevant variables become marginal, lead to an analogous pair of Fisher relations for logarithmic-correction exponents. Implications of a similar distinction between length scales in percolation theory above d_c and for the Ginzburg criterion are briefly discussed.Comment: Published version has 6 pages, 2 figure

Looking for the Logarithms in Four-Dimensional Nambu-Jona-Lasinio Models

We study the problem of triviality in the four dimensional Nambu-Jona-Lasinio model with discrete chiral symmetry using both large-N expansions and lattice simulations. We find that logarithmic corrections to scaling appear in the equation of state as predicted by the large-N expansion. The data from $16^4$ lattice simulations is sufficiently accurate to distinguish logarithmically trivial scaling from power law scaling. Simulations on different lattice sizes reveal an interesting interplay of finite size effects and triviality. We argue that such effects are qualitatively different for theories based on fundamental scalar rather than fermion fields. Several lessons learned here can be applied to simulations and analyses of more challenging field theories.Comment: 25 pages, 14 ps figure

Role of Fourier Modes in Finite-Size Scaling above the Upper Critical Dimension

Renormalization-group theory stands, since over 40 years, as one of the pillars of modern physics. As such, there should be no remaining doubt regarding its validity. However, finite-size scaling, which derives from it, has long been poorly understood above the upper critical dimension $d_c$ in models with free boundary conditions. Besides its fundamental significance for scaling theories, the issue is important at a practical level because finite-size, statistical-physics systems, with free boundaries above $d_c$, are experimentally accessible with long-range interactions. Here we address the roles played by Fourier modes for such systems and show that the current phenomenological picture is not supported for all thermodynamic observables either with free or periodic boundaries. Instead, the correct picture emerges from a sector of the renormalization group hitherto considered unphysical.Comment: 10 pages, 2 figure

International Pediatric Otolaryngology Group (IPOG) consensus recommendations: Hearing loss in the pediatric patient

OBJECTIVE To provide recommendations for the workup of hearing loss in the pediatric patient. METHODS Expert opinion by the members of the International Pediatric Otolaryngology Group. RESULTS Consensus recommendations include initial screening and diagnosis as well as the workup of sensorineural, conductive and mixed hearing loss in children. The consensus statement discusses the role of genetic testing and imaging and provides algorithms to guide the workup of children with hearing loss. CONCLUSION The workup of children with hearing loss can be guided by the recommendations provided herei

The Ctf18 RFC-like complex positions yeast telomeres but does not specify their replication time

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