Related papers: Tailoring a pair of pants: the phase tropical vers…

We develop the notion of the good pants homology and show that it agrees with the standard homology on closed surfaces (the good pants are pairs of pants whose cuffs have the length nearly equal to some large number R). Combined with our…

We evaluate the thermodynamic properties of the 4-state antiferromagnetic Potts model on the Union- Jack lattice using tensor-based numerical methods. We present strong evidence for a previously unknown, "entropy-driven," finite-temperature…

We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both…

The full complex phase structure of the meson-baryon reaction amplitude in coupled channels approach is investigated, including also the photon-baryon channel. The result may be viewed as a generalization of the well-known Watson's theorem.…

Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological…

Ultracold mixtures of different atomic species have great promise for realizing novel many-body phenomena. In a binary mixture of femions with a large mass difference and repulsive interspecies interactions, a disordered Mott insulator…

The open book decompositions of the 3-sphere whose pages are pairs of pants have been fully understood for some time, through the lens of contact geometry. The purpose of this note is to exhibit a purely topological derivation of the…

We study in this work flat surfaces with conical singularities, that is, surfaces provided with a flat structure with conical singular points. Finding good parameters for these surfaces in the general case is an open question. We give an…

We discuss the so-called two-temperature model in linear thermoelasticity and provide a Hilbert space framework for proving well-posedness of the equations under consideration. With the abstract perspective of evolutionary equations, the…

We show that fermionic dipoles in a two-layer geometry form Cooper pairs with both singlet and triplet components, when they are tilted with respect to the normal of the planes. The mixed parity pairing arises because the interaction…

We report new results on complex-temperature properties of Ising models. These include studies of the $s=1/2$ model on triangular, honeycomb, kagom\'e, $3 \cdot 12^2$, and $4 \cdot 8^2$ lattices. We elucidate the complex--$T$ phase diagrams…

We develop the theory of the resonant formation of coupled topological-collective coherent modes in the presence of a quantized trap and classical external field. The coupling between the topological and the collective modes can be linear…

We prove that the half plane version of the uniform infinite planar triangulation (UIPT) is recurrent. The key ingredients of the proof are a construction of a new full plane extension of the half plane UIPT, based on a natural…

This note is about the geometry of the pants graph P(S), a natural simplicial graph associated to a finite type topological surface S where vertices represents pants decompositions. The main result in this note ascserts that for a…

We present a new characterization of the shape equivalent class and the Littlewood-Richardson correspondence of Young tableaux in terms of tropical (ultradiscrete) integrable systems. As an application, an alternative proof of the "shape…

Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard, this article presents a fast algorithm for identifying the…

Overlap with the separable state is introduced in this paper for the purpose of characterizing the overall correlation in many-body systems. This definition has clear geometric and physical meaning, and moreover can be considered as the…

We consider in this paper the general properties of laminates designed to be isotropic in extension and in bending and with a coupling between the in- and out-of plane responses. In particular, we analyze the mathematical properties of the…

We give several characterizations of stable intersections of tropical cycles and establish their fundamental properties. We prove that the stable intersection of two tropical varieties is the tropicalization of the intersection of the…

The n-dimensional pair of pants is defined to be the complement of n+2 generic hyperplanes in CP^n. We construct an immersed Lagrangian sphere in the pair of pants and compute its endomorphism A_{\infty} algebra in the Fukaya category. On…