Related papers: A matrix model with a singular weight and Painleve…
The Ising model in two dimensions with special toroidal boundary conditions is analyzed. These boundary condition, which we call duality twisted boundary conditions, may be interpreted as inserting a specific defect line ("seam") in the…
The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as…
We identify the Riemann Xi function as the Baker-Akhiezer function for a (p,1) two matrix model as p goes to infinity. We solve the two matrix model using biorthogonal polynomials and study the zeros of the polynomials in the double scaling…
The large-N behavior of Yang-Mills and generalized Yang-Mills theories in the double-scaling limit is investigated. By the double-scaling limit, it is meant that the area of the manifold on which the theory is defined, is itself a function…
The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to…
We introduce a randomized iterative fragmentation procedure for finite metric spaces, which is guaranteed to result in a polynomially large subset that is $D$-equivalent to an ultrametric, where $D\in (2,\infty)$ is a prescribed target…
Nonlinear Drude weight (NLDW) is a new concept which characterizes the nonlinear transport in quantum many-body systems. We investigate these weights for the spin-1/2 XXZ chain in the critical regime. The effects of the…
This thesis deals with the construction of conserved charges for asymptotically flat spacetimes at spatial infinity in four spacetime dimensions in a hopefully pedagogical way. As a first motivation of this work, it highlights the…
After reviewing the Hermitian one matrix model, we will give a brief introduction to the Hermitian two matrix model and present a summary of some recent results on the asymptotic behavior of the two matrix model with a quartic potential. In…
We study the double scaling limit of mKdV type, realized in the two-cut Hermitian matrix model. Building on the work of Periwal and Shevitz and of Nappi, we find an exact solution including all odd scaling operators, in terms of a hierarchy…
We study the asymptotics of recurrence coefficients for monic orthogonal polynomials $\pi_n(z)$ with the quartic exponential weight $\exp[-N(\frac 12 z^2+\frac 14 tz^4)]$, where $t\in {\mathbb C}$ and $N\in{\mathbb N}$, $N\to\infty$. Our…
O(N) vector sigma models possessing catastrophes in their action are studied. Coupling the limit N --> infinity with an appropriate scaling behaviour of the coupling constants, the partition function develops a singular factor. This is a…
We show that the one-parameter family of special solutions of P$_\mathrm{II}$, the second Painlev\'e equation, constructed from the Airy functions, as well as associated solutions of P$_\mathrm{XXXIV}$ and S$_\mathrm{II}$, can be expressed…
We study Matrix Quantum Mechanics on the Euclidean time orbifold $S_1/\mathbb{Z}_2$. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two…
We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean $AdS_2$ background using the matrix model description recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that the…
Strong asymptotics of polynomials orthogonal on the unit circle with respect to a weight of the form $$ W(z) = w(z) \prod_{k=1}^m |z-a_k|^{2\beta_k}, \quad |z|=1, \quad |a_k|=1, \quad \beta_k>-1/2, \quad k=1, ..., m, $$ where $w(z)>0$ for…
We study the order-disorder transition in two-dimensional incompressible systems of motile particles with alignment interactions through extensive numerical simulations of the incompressible Toner-Tu (ITT) field theory and a detailed…
We consider $\mathcal N=2$ conformal QCD in four dimensions and the one-point correlator of a class of chiral primaries with the circular $\frac{1}{2}$-BPS Maldacena-Wilson loop. We analyze a recently introduced double scaling limit where…
Using matrix-model methods we study three different N=2 models: U(N) x U(N) with matter in the bifundamental representation, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. We find…
In this article, we derive the asymptotic expansion, up to an arbitrary order in theory, for the solution of a two-dimensional elliptic equation with strongly anisotropic diffusion coefficients along different directions, subject to the…