Star--Matrix Models

The star-matrix models are difficult to solve due to the multiple powers of the Vandermonde determinants in the partition function. We apply to these models a modified Q-matrix approach and we get results consistent with those obtained by other methods.As examples we study the inhomogenous gaussian model on Bethe tree and matrix $q$-Potts-like model. For the last model in the special cases $q=2$ and $q=3$, we write down explicit formulas which determinate the critical behaviour of the system.For $q=2$ we argue that the critical behaviour is indeed that of the Ising model on the $\phi^3$ lattice.Comment: 15 pages, Latex (to appear in Mod.Phys.Lett.

Quantum Chaos in Multi-Matrix Models

We propose a possible resolution for the problem of why the semicircular law is not observed, whilst the random matrix hypothesis describes well the fluctuation of energy spectra. We show in the random 2-matrix model that the interactions between the quantum subsystems alter the semicircular law of level density. We consider also other types of interactions in the chain- and star-multimatrix models. The connection with the Calogero-Sutherland models is briefly discussed.Comment: 15 pages, Latex; 1 figure (available from author

Multi-Matrix Models: Integrability Properties and Topological Content

We analyze multi--matrix chain models. They can be considered as multi--component Toda lattice hierarchies subject to suitable coupling conditions. The extension of such models to include extra discrete states requires a weak form of integrability. The discrete states of the $q$--matrix model are organized in representations of $sl_q$. We solve exactly the Gaussian--type models, of which we compute several all-genus correlators. Among the latter models one can classify also the discretized $c=1$ string theory, which we revisit using Toda lattice hierarchy methods. Finally we analyze the topological field theory content of the $2q$--matrix models: we define primary fields (which are $\infty^q$), metrics and structure constants and prove that they satisfy the axioms of topological field theories. We outline a possible method to extract interesting topological field theories with a finite number of primaries.Comment: 31 pages, Late

Toda lattice realization of integrable hierarchies

We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudodifferential Lax operator, can be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda lattice hierarchy seems to be as general as the Drinfeld--Sokolov realization.Comment: 11 pages, Latex (minor changes, to appear in Lett.Math.Phys.

Magnetic Properties of Co2MnSiCo_2MnSi Compound with Tb Impurities

In this paper we report our experimental and theoretical studies on the effect of Tb impurity on the magnetic properties of the Heusler half metallic ferromagnet $Co_2MnSi$. The analysis of the band structures of the doped alloy shows that the half-metallic properties are completely conserved if Tb substitute Mn atoms, this effect being determined through the coupling between the R(4f) spin with the Mn(3d) itinerant electron spins. We evaluate the strength of such a coupling by calculating, in an ab initio fashion, the total energy of $Co_{16}Mn_7TbSi_8$ compound for a parallel and antiparallel f-d coupling. The experimental magnetic moments are in good agreement with the calculated ones in case of ferrimagnetic ordering

Quantum chaos in multi-matrix models

Consiglio Nazionale delle Ricerche (CNR). Biblioteca Centrale / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

The Effect of Gd Impurities on the Physical Properties of Half-Metallic Ferromagnet Co2MnSiCo_2MnSi

In this paper we report our experimental and theoretical studies on the effect of Gd impurity on the physical properties of the Heusler half-metallic ferromagnet $Co_2MnSi$. The analysis of the band structures of the doped alloy shows that the half-metallic properties are completely conserved if Gd substitutes Mn atoms. This effect is not determined by the spin-orbit interaction, but through the coupling between the R(4f) spin with the Mn(3d) itinerant electron spins. We evaluate the strength of such a coupling by calculating, in an ab initio fashion, the total energy of $Co_{16}GdMn_7Si_8$ compound for a parallel and antiparallel f-d coupling. The obtained magnetic moments of Co or Mn sites are in good agreement with the experimental ones