Related papers: Two-Matrix model with ABAB interaction
We consider Majorana lattices with two-site interactions consisting of a general function of the fermion bilinear. The models are exactly solvable in the limit of a large number of on-site fermions. The four-site chain exhibits a quantum…
In this thesis generalizations of matrix and eigenvalue models involving supersymmetry are discussed. Following a brief review of the Hermitian one matrix model, the c=-2 matrix model is considered. Built from a matrix valued superfield…
A class of the $D=4$ gravity models describing a coupled system of $n$ Abelian vector fields and the symmetric $n \times n$ matrix generalizations of the dilaton and Kalb-Ramond fields is considered. It is shown that the Pecci-Quinn axion…
We study the hermitean and normal two matrix models in planar approximation for an arbitrary number of eigenvalue supports. Its planar graph interpretation is given. The study reveals a general structure of the underlying analytic complex…
In the Hamiltonian picture, free spin-$1/2$ Dirac fermions on a bipartite lattice have an $O(4)$ (spin-charge) symmetry. Here we construct an interacting lattice model with an interaction $V$, which is similar to the Hubbard interaction but…
We present some arguments showing spectrum doubling of matrix models in the limit $N\to\infty$ which is connected with fermionic determinant behaviour. The problems are similar to ones encountered in the lattice gauge theories with chiral…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
Two-field mimetic gravity was recently realized by looking at the singular limit of the conformal transformation between the auxiliary metric and the physical metric with two scalar fields involved. In this paper, we reanalyze the singular…
A new one-dimensional fermion model depending on two independent interaction parameters is formulated and solved exactly by the Bethe ansatz method. The Hamiltonian of the model contains the Hubbard interaction and correlated hopping as…
We study the large-$N$ limit of adjoint fermion one-matrix models. We find one-cut solutions of the loop equations for the correlators of these models and show that they exhibit third order phase transitions associated with $m$-th order…
The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different…
We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimensions due to crossing symmetry and unitarity. In this way we establish rigorous bounds on the cubic couplings of a given theory with…
We study a hermitian $(n+1)$-matrix model with plaquette interaction, $\sum_{i=1}^n MA_iMA_i$. By means of a conformal transformation we rewrite the model as an $O(n)$ model on a random lattice with a non polynomial potential. This allows…
We study two dimensional conformal field theories in the semiclassical limit. In this limit, the four-point function is dominated by intermediate primaries of particular weights along with their descendants, and the crossing equations…
We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to $\hat c<1 $ matter…
We introduce a basis for a bi-dimensional finite matrix calculus and a bi-dimensional finite matrix action principle. As an application, we analyze scalar and spinorial fields in $D=4n+2$ in this approach. We verify that to establish a…
We exactly solve a special matrix model of dually weighted planar graphs describing pure two-dimensional quantum gravity with an R^2 interaction. It permits us to study the intermediate regimes between the gravitating and flat metric. Flat…
We consider a model of discretized 2d gravity interacting with Ising spins where phase boundaries are restricted to have minimal length and show analytically that the critical exponent $\gamma= 1/3$ at the spin transition point. The model…
By introducing a $\int dt \, g\left(\Tr \Phi^2(t)\right)^2$ term into the action of the $c=1$ matrix model of two-dimensional quantum gravity, we find a new critical behavior for random surfaces. The planar limit of the path integral…
We investigate Matrix theory in the large-N limit following the conjectured correspondence between Matrix theory and supergravity on the near-horizon limit of the D0-brane background. We analyze the complete fermionic spectrum of…