arXiv subjects

A. Matytsin

Publications and source records attributed to A. Matytsin.

3 recordsLinked to original sources

arXiv1997

The Two-Dimensional O(2) Model on a Random Planar Lattice at Strong Coupling

The large spacing phase of the infinite random matrix chain, which represents the strongly coupled two-dimensional O(2) model on a random planar lattice, is explored. A class of solutions valid for large lattice spacings is constructed. It is proved that these solutions exhibit the critical exponents characteristic of pure two-dimensional gravity. The character expansion for the chain model is developed and an order parameter governing the Kosterlitz--Thouless phase transition is identified.

hep-th↗

arXiv1996

Kosterlitz--Thouless Phase Transitions on Discretized Random Surfaces

The large N limit of a one-dimensional infinite chain of random matrices is investigated. It is found that in addition to the expected Kosterlitz--Thouless phase transition this model exhibits an infinite series of phase transitions at special values of the lattice spacing ε_{pq}=\sin(πp/2q). An unusual property of these transitions is that they are totally invisible in the double scaling limit. A method which allows us to explore the transition regions analytically and to determine certain critical exponents is developed. It is argued that phase transitions of this kind can be induced by the interaction of two-dimensional vortices with curvature defects of a fluctuating random lattice.

hep-th↗

arXiv1993

On the Large N Limit of the Itzykson-Zuber Integral

We study the large N limit of the Itzykson -- Zuber integral and show that the leading term is given by the exponent of an action functional for the complex inviscid Burgers (Hopf) equation evaluated on its particular classical solution; the eigenvalue densities that enter in the IZ integral being the imaginary parts of the boundary values of this solution. We show how this result can be applied to ``induced QCD" with an arbitrary potential $U(x)$. We find that for a nonsingular $U(x)$ in one dimension the eigenvalue density $ρ(x)$ at the saddle point is the solution of the functional equation $G_{+}(G_{-}(x))=G_{-}(G_{+}(x))=x$, where $G_{\pm}(x) \equiv {1\over{2}}U^{\prime}(x)\pm iπρ(x)$. As an illustration we present a number of new particular solutions of the $c=1$ matrix model on a discrete real line.

hep-th↗