Following a novel approach to solve sofar unsolved Ising problems like the 3Dproblem for the simple cubic isotropic lattice, the authors brought forward a potential solution. This potential solution is analyzed to illustrate various aspects of the approach and is replaced by another.

We develop a theory of quasiparticle localization in superconductors in situations without spin rotation invariance. We discuss the existence and properties of superconducting phases with localized/delocalized quasiparticle excitations in such systems in various dimensionalities. Implications for a variety of experimental systems, and to the properties of random Ising models in two dimensions, ...

We study the Glauber dynamics for Ising model on (sequences of) dense graphs. We view the dense graphs through the lens of graphons [19]. For the ferromagnetic Ising model with inverse temperature β on a convergent sequence of graphs {Gn} with limit graphon W we show fast mixing of the Glauber dynamics if βλ1(W ) < 1 and slow (torpid) mixing if βλ1(W ) > 1 (where λ1(W ) is the largest eigenvalu...

A sharp-threshold theorem is proved for box-crossing probabilities on the square lattice. The models in question are the random-cluster model near the self-dual point psd(q) = √ q/(1+ √ q), the Ising model with external field, and the coloured random-cluster model. The principal technique is an extension of the influence theorem for monotonic probability measures applied to increasing events wi...

I describe the use of techniques based on composite rotations to develop controlled phase gates in which the effects of weak Ising couplings are suppressed. A tailored composite phase gate is described which both suppresses weak couplings and is relatively insensitive to systematic errors in the size of strong couplings.

Results about long-range order behaviour are obtained for systems in arbitrary dimension with a wide class of spin-spin long-range interactions , without assuming the reeection positivity property.