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We show how to couple two critical Q-state Potts models to yield a new self-dual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed…
Adapting a method recently proposed by C. Marboe and D. Volin for ${\cal N}$=4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling expansion of the spectrum of anomalous dimensions in the $sl(2)$-like sector of planar…
We present a review of the work L. Raymond from 1995. The review aims at making this work more accessible and offers adaptations of some statements and proofs. In addition, this review forms an applicable framework for the complete solution…
Let $\Omega\subset\mathbb{R}^n$ be a strictly convex domain with smooth boundary and diameter $D$. The fundamental gap conjecture claims that if $V:\bar\Omega\to\mathbb{R}$ is convex, then the spectral gap of the Schr\"odinger operator…
Superfluidity in the cold atomic two-species Fermi gas system in the unitary limit of infinite scattering length remains incompletely understood. In particular, a pseudogap phase has been proposed to exist above the superfluid critical…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
Using the notion of spectral flow, we suggest a simple approach to various asymptotic problems involving eigenvalues in the gaps of the essential spectrum of self-adjoint operators. Our approach uses some elements of the spectral shift…
Finding the exact integrality gap $\alpha$ for the LP relaxation of the 2-edge-connected spanning multigraph problem (2EC) is closely related to the same problem for the Held-Karp relaxation of the metric traveling salesman problem (TSP).…
The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…
Computational techniques are extensively applied in nonlinear science. However, while the use of computers for research has been expressive, the evaluation of numerical results does not grow in the same pace. Hammel et al. (Journal of…
We numerically study the SU(2)$\otimes$SU(2) symmetric spin-orbit coupled model as a lower symmetric generalization of the SU(4) exchange model. On the symmetric line with respect to the spin and orbit, our result shows the essentially…
Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding loops crossing a line through a given number of points, $n$. Meanders are considered distinct up to any smooth deformation leaving the line fixed.…
How to design fair and (computationally) efficient voting rules is a central challenge in Computational Social Choice. In this paper, we aim at designing efficient algorithms for computing most equitable rules for large classes of…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
Fix a P.V. number $\lambda ^{-1}>1.$ Given $\mathbf{p}=(p_{1},\cdots,p_{m})\in \mathbb{N}^{m}$, $\mathbf{b}=(b_{1},\cdots,b_{m})\in \mathbb{Q^{m}$, for the self-similar set $E_{\mathbf{p},\mathbf{b}}=\cup_{i=1}^{m}(\lambda…
A challenge - and opportunity - is offered to the Hubbard Model community of solutions extant for the strong coupling region. A rigorous and quantitatively demanding test - a Computer Lab - is presented based on certain exact results for…
multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…
This work proposes a novel enumeration algorithm for computing the integrality gap of small instances of the subtour elimination formulation for the Asymmetric Traveling Salesman Problem (ATSP). The core idea is to enumerate pairs of…
Superconductivity is realized by opening a gap in the superconducting state. The gap symmetry is crucial in understanding the underlying superconductivity mechanism. The magnitude and the phase are essential in fully characterizing the…
A $\theta$ term, which couples to topological charge, is added to the lattice $CP^{N-1}$ model. The strong-coupling character expansion is developed. The series for the free energy and mass gap are respectively computed to tenth order and…