Related papers: Second and Third Order Observables of the Two-Matr…
We construct the complex multi-matrix model with W-representation and calculate the correlators. We establish the correspondence between the connected correlators and length-2n q-colored Dyck walks in Fredkin spin chain and discuss the…
In this work we obtain the planar free energy for the Hermitian one-matrix model with various choices of the potential. We accomplish this by applying an approach that bypasses the usual diagonalization of the matrices and the introduction…
We construct a two-tensor model with order-3 and present its $W$-representation. Moreover we derive the compact expressions of correlators from the $W$-representation and analyze the free energy in large $N$ limit. In addition, we establish…
We first study a free particle on an $(n-1)$-sphere in an extended phase space, where the originally second-class Hamiltonian and constraints are now in strong involution. This allows for a Schr\"odinger representation and a Hamilton-Jacobi…
We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/ N expansion of the nonmixed correlation functions and give a new…
An integral form of the discrete superloop equations for the supereigenvalue model of Alvarez-Gaume, Itoyama, Manes and Zadra is given. By a change of variables from coupling constants to moments we find a compact form of the planar…
We suggest that some observational features of high-energy radiation from pulsars should be explained in terms of three dimensional geometric models, e.g. the phase-resolved X-ray and $\gamma$-ray spectra and the energy dependent light…
A second order extrapolation method is presented for shell model calculations, where shell model energies of truncated spaces are well described as a function of energy variance by quadratic curves and exact shell model energies can be…
We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to…
In the present paper we consider controllability and observability of second order linear time invariant systems in matrix form. Without reducing into first order systems we show how the classical conditions for first order linear systems…
We study the full set of planar Green's functions for a two-matrix model using the language of functions of non-commuting variables. Both the standard Schwinger-Dyson equations and equations determining connected Green's functions can be…
We compute the planar limit of both the free energy and the expectation value of the $1/2$ BPS Wilson loop for four dimensional ${\cal N}=2$ superconformal quiver theories, with a product of SU($N$)s as gauge group and bi-fundamental…
We show how to expand the free energy of a matrix model coupled to arbitrary matter in powers of the matter coupling constant. Concentrating on $\nu$ uncoupled Ising models---which have central charge $\nu/2$---we work out the expansion to…
We investigate phase transitions in three dimensional scalar matrix models, with special emphasis on complex $2 \times 2$ matrices. The universal equation of state for weak first order phase transitions is computed. We also study the coarse…
We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We…
The two-body t-matrix is calculated directly as function of two vector momenta for different Malfliet-Tjon type potentials. At a few hundred MeV projectile energy the total amplitude is quite a smooth function showing only a strong peak in…
We study energy minimizers of the Ginzburg-Landau (GL) free energy, a fundamental model of superconductivity. We address the high-$\kappa$ regime, the regime of a large GL parameter, in which energy minimizers exhibit vortex structures…
We study a two-loop contribution to the dark-matter trispectrum and evaluate it numerically using an infrared-safe integrand. The calculation is organized as an expansion around a fixed reference cosmology: the linear matter power spectrum…
Using a model-independent low-energy effective field theory, we calculate the free energy of three-dimensional antiferromagnets in a combination of mutually perpendicular external magnetic and staggered fields at the…
The two matrix model is considered, with measure given by the exponential of a sum of polynomials in two different variables. It is shown how to derive a sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding…