Tootfinder

Dimerization in $O(n)$-invariant quantum spin chains
J. E. Bj\"ornberg, K. Ryan
https://arxiv.org/abs/2506.06103 https://arxiv.o…

Dimerization in $O(n)$-invariant quantum spin chains
We establish dimerization in $O(n)$-invariant quantum spin chains with big enough $n$, in a large part of the phase diagram where this result is expected. This includes identifying two distinct ground states which are translations of one unit of eachother, and which both have exponentially decaying correlations. Our method relies on a probabilistic representation of the quantum system in terms of random loops, and an adaptation of a method developed for loop $O(n)$ models on the hexagonal latti…

Pushforwards in Inverse Homotopical Diagrams
Chris Kapulkin, Yufeng Li
https://arxiv.org/abs/2506.04472 https://arxiv.org/pdf/2506.04…

Pushforwards in Inverse Homotopical Diagrams
We establish a sufficient condition for the category of homotopical inverse diagrams to be closed under pushforward inside the category of inverse diagrams in a fibration category.

Upper bounds on class numbers of real quadratic fields
Riccardo Bernardini
https://arxiv.org/abs/2506.21301 https://arxiv.org/pdf/250…

Upper bounds on class numbers of real quadratic fields
We prove that, for any $\varepsilon>0$, the number of real quadratic fields $\mathbb{Q}(\sqrt{d})$ of discriminant $d

Counting biquadratic number fields with quaternionic and dihedral extensions
Louis M. Gaudet, Siman Wong
https://arxiv.org/abs/2506.21522 https://

Counting biquadratic number fields with quaternionic and dihedral extensions
We establish asymptotic formulae for the number of biquadratic number fields of bounded discriminant that can be embedded into a quaternionic or a dihedral extension. To prove these results, we express the solvability of these inverse Galois problems in terms of Hilbert symbols, and then apply a method of Heath-Brown to bound sums of linked quadratic characters.