2:34 AM
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Let $X$ be a smooth complex projective variety of dimension $n\geq2$, let $\mathfrak{E}=(E,\varphi)$ be a Higgs bundle over $X$ of rank $r\geq2$. Does exists a Higgs quotient sheaf $\mathcal{Q}$ of $\mathfrak{E}$ of rank $p$, for any $p\in\{1,\dotsc,r-1\}$? For clarity: Higgs sheaf \$\mathfrak{E...

In mathematics, a Higgs bundle is a pair ( E , φ ) {\displaystyle (E,\varphi )} consisting of a holomorphic vector bundle E and a Higgs field φ {\displaystyle \varphi } , a holomorphic 1-form taking values in End(E) such that φ ∧ φ = 0 {\displaystyle \varphi \wedge \varphi =0} . Such pairs were introduced by Nigel Hitchin (1987), who named the field φ {\displaystyle...

5 hours later…
7:32 AM
I have noticed this question in the HNQ list. It has no top-level tag: Interesting and surprising applications of the Ising Model.
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One of the most famous models in physics is the Ising model, invented by Wilhelm Lenz as a PhD problem to his student Ernst Ising. The one-dimensional version of it was solved in Ising's thesis in 1924; later, in 1944, Lars Onsager solved the two-dimensional case in the absense of external magnet...