Related papers: Phases in WLZZ Matrix Models
Among other interesting results, in a recent paper, Katzourakis analysed the phenomenon of separation of the solutions to the infinity Laplace system to phases with qualitatively different behavior in the case of the 2 dimensional infinity…
We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe their basis activities, and we prove some basic structural…
Multivalued projections are applied to the study of weighted least squares solutions of linear relations equations (or inclusions) and some of its applications. To this end a matrix representation of multivalued projections with respect to…
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant…
We introduce two-dimensional logics based on \L{}ukasiewicz and G\"{o}del logics to formalize paraconsistent fuzzy reasoning. The logics are interpreted on matrices, where the common underlying structure is the bi-lattice (twisted) product…
We investigate the relationship between supersymmetric gauge theories with moduli spaces and matrix models. Particular attention is given to situations where the moduli space gets quantum corrected. These corrections are controlled by…
This article considers the classification of matrix superpotentials that corresponds to exactly solvable systems of Schrodinger equations. Superpotentials of the following form are considered: $W_k = kQ + P + \frac1kR$, where $k$ ---…
We review the description of scalar field theories on fuzzy spaces by Hermitian random matrix models. After reminding the reader of the relevant aspects of the random matrix theory and construction of the fuzzy spaces, we summarize the most…
We study dynamics of a membrane and its matrix regularisation. We present the matrix regularisation for a membrane propagating in a curved space-time geometry in the presence of an arbitrary 3-form field. In the matrix regularisation, we…
Swartz proved that any matroid can be realized as the intersection lattice of an arrangement of codimension one homotopy spheres on a sphere. This was an unexpected extension from the oriented matroid case, but unfortunately the…
We propose a model for explanation the "domain-wall" type configuration states in binary lipid mixtures of cationic and neutral lipids, associated with observed relaxation effects in their aggregates. We apply the analogy with formation of…
We consider the geometric structures on the moduli space of static finite energy solutions to the 2+1 dimensional unitary chiral model with the Wess-Zummino-Witten (WZW) term. It is shown that the magnetic field induced by the WZW term…
In the paper, we introduce a matrix method to constructively determine spaces of polynomial solutions (in general, multiplied by exponentials) to a system of constant coefficient linear PDE's with polynomial (multiplied by exponentials)…
We investigate a unitary matrix model with a complex potential with Fisher-Hartwig singularities. We show that the model exhibits finite-$N$ phase transitions. The order of the phase transition is coupling-dependent. At large-$N$, these…
Four-dimensional manifolds with changing signature are obtained by taking the large $N$ limit of fuzzy $CP^2$ solutions to a Lorentzian matrix model. The regions of Lorentzian signature give toy models of closed universes which exhibit…
The techniques developed for matrix models and fuzzy geometry are powerful tools for representing strings and membranes in quantum physics. We study the representation of fuzzy surfaces using these techniques. This involves constructing…
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B)…
In the extended (1 + 4) -dimensional space (T;X,Y,Z,S)-(time-space-interval) it is considered a model joining electromagnetic and gravitational fields. For the equations circumscribing these fields, the exact solutions appropriated to dot…
We solve the one-dimensional Schr\"odinger equation for the bound states of two potential models with a rich structure as shown by their "spectral phase diagram". These potentials do not belong to the well-known class of exactly solvable…
The set of modular invariants that can be obtained from Galois transformations is investigated systematically for WZW models. It is shown that a large subset of Galois modular invariants coincides with simple current invariants. For…