相关论文: Duality of a Generalized Gauge Invariant Ising Mod…
Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following…
This is a short note on generalized $G_2$-structures obtained as a consequence of a $T$-dual construction given in a previous work of the authors together with Leonardo Soriani. Given classical $G_2$-structure on certain seven dimensional…
A method for implementing non-Abelian duality on string backgrounds is given. It is shown that a direct generalisation of the familiar Abelian duality induces an extra local symmetry in the gauge invariant theory. The non-Abelian isometry…
Mimicking the idea of the generalized Hamming weight of linear codes, we introduce a new lattice invariant, the generalized theta series. Applications range from identifying stable lattices to the lattice isomorphism problem. Moreover, we…
Random bond Ising systems on a general hierarchical lattice are considered. Interesting inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These lead to upper bounds on the…
A particular $U(N)$ gauge theory defined on the three dimensional dodecahedral lattice is shown to correspond to a model of oriented self-avoiding surfaces. Using large $N$ reduction it is argued that the model is partially soluble in the…
Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path) integrals by gauge theory or non-linear…
We study the pseudoduality transformation in supersymmetric sigma models. We generalize the classical construction of pseudoduality transformation to supersymmetric case. We perform this both by component expansion method on manifold M and…
We investigate topological T-duality in the framework of non-abelian gerbes and higher gauge groups. We show that this framework admits the gluing of locally defined T-duals, in situations where no globally defined ("geometric") T-duals…
We consider the symmetric two-state 16-vertex model on the square lattice whose vertex weights are invariant under any permutation of adjacent edge states. The vertex-weight parameters are restricted to a critical manifold which is…
Which polygons admit two (or more) distinct lattice tilings of the plane? We call such polygons double tiles. It is well-known that a lattice tiling is always combinatorially isomorphic either to a grid of squares or to a grid of regular…
Statistical mechanics describes interaction between particles of a physical system. Particle properties of the system can be modelled with a random field on a lattice and studied at different distance scales using renormalization group…
The dual normal factor graph and the factor graph duality theorem have been considered for discrete graphical models. In this paper, we show an application of the factor graph duality theorem to continuous graphical models. Specifically, we…
We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and…
Phase transition of the Ising model is investigated on a planar lattice that has a fractal structure. On the lattice, the number of bonds that cross the border of a finite area is doubled when the linear size of the area is extended by a…
It is known that electric-magnetic duality transformations are symmetries of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. In Seiberg-Witten theory the solutions to these equations come in certain sets according to…
(Anti)self-dual solutions of the scale invariant SU(2) gauged Grassmanian model are sought. A stronger (anti)selfduality condition for this system is defined, referred to as strong self-duality, and spherically symmetric solutions of this…
This brief review surveys recent progress driven by the gauge/Yang-Baxter equation (YBE) correspondence. This connection has proven to be a powerful tool for discovering novel integrable lattice spin models in statistical mechanics by…
We give a global formulation of the coupling of four-dimensional scalar sigma models to Abelian gauge fields for the generalized situation when the "duality structure" of the Abelian gauge theory is described by a flat symplectic vector…
Lattice gauge theory is an important framework for studying gauge theories that arise in the Standard Model and condensed matter physics. Yet many systems (or regimes of those systems) are difficult to study using conventional techniques,…