We use a transformation due to Percus to give a simple derivation of the Griffiths, Hurst, and Sherman, and some other new inequalities, for Ising ferromagnets with pair interactions. The proof makes use of the Griffiths, Kelly, and Sherman and the Fortuin, Kasteleyn, and Ginibre inequalities.

We prove a conjecture of Griffiths on the quasi-projectivity images period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop theory analytic spaces and coherent sheaves that are definable with respect to given structure, GAGA-type theorem algebraizing complex algebraic spaces. then combine this theorems Artin show proper algebraic. Applying maps, ...

A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D q-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with the lattice size in a broad range of temperatures. However, only relatively small lattice sizes could be considered, so one can wonder whether this Griffiths ph...

Robert Griffiths has recently addressed, within the framework of a ‘consistent quantum theory’ that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-...

The Griffiths conjecture asserts that every ample vector bundle $E$ over a compact complex manifold $S$ admits hermitian metric with positive curvature in the sense of Griffiths. In this article we give sufficient condition for on $\mathcal{O}_{\mathbb{P}(E^*)}(1)$ to induce $L^2$-metric $E$. This result suggests study relative K\ahler-Ricci flow fibration $\mathbb{P}(E^*)\to S$. We define and ...