Related papers: Combinatorial Invariants from Four Dimensional Lat…
It is an open question to give a combinatorial interpretation of the Falk invariant of a hyperplane arrangement, i.e. the third rank of successive quotients in the lower central series of the fundamental group of the arrangement. In this…
Combinatorial gauge symmetry is a principle that allows us to construct lattice gauge theories with two key and distinguishing properties: a) only one- and two-body interactions are needed; and b) the symmetry is exact rather than emergent…
A lattice gauge theory with an action polynomial in independent field variables is considered. The link variables are described by unconstrained complex matrices instead of unitary ones. A mechanism which permits to switch off in the…
The aim of the paper is to obtain a description of the selfadjoint subspace of the one-speed Boltzmann operator. It is proved that this subspace is nontrivial if the collision integral is polynomial and the multiplication coefficient has a…
We study random composite structures considered up to symmetry that are sampled according to weights on the inner and outer structures. This model may be viewed as an unlabelled version of Gibbs partitions and encompasses multisets of…
We investigate the electromagnetic duality properties of an abelian gauge theory on a compact oriented four-manifold by analysing the behaviour of a generalised partition function under modular transformations of the dimensionless coupling…
Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two…
It is known, that every function on the unit sphere in $\bbr^n$, which is invariant under rotations about some coordinate axis, is completely determined by a function of one variable. Similar results, when invariance of a function reduces…
Using the self-dual lattice method, we make a systematic search for modular invariant partition functions of the affine algebras $g\*{(1)}$ of $g=A_2$, $A_1+A_1$, $G_2$, and $C_2$. Unlike previous computer searches, this method is…
In this paper, we build on the biquasiles and dual graph diagrams introduced in arXiv:1610.06969. We introduce \textit{biquasile Boltzmann weights} that enhance the previous knot coloring invariant defined in terms of finite biquasiles and…
We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of…
We study the Boltzmann equation in a smooth bounded domain featuring a mixed boundary condition. Specifically, gas particles experience specular reflection in two parallel plates, while diffusive reflection occurs in the remaining portion…
We introduce two exotic lattice models on a general spatial graph. The first one is a matter theory of a compact Lifshitz scalar field, while the second one is a certain rank-2 $U(1)$ gauge theory of fractons. Both lattice models are…
We explore the phase structure and symmetry breaking in four-dimensional SU(3) gauge theory with one spatial compact dimension on the lattice in the presence of fermions in the adjoint and fundamental representations with general boundary…
We investigate the phase diagram and critical behavior of three-dimensional multicomponent Abelian-Higgs models, in which an N-component complex field z_x^a of unit length and charge is coupled to compact quantum electrodynamics in the…
We show that the partition function of many classical models with continuous degrees of freedom, e.g. abelian lattice gauge theories and statistical mechanical models, can be written as the partition function of an (enlarged)…
We investigate the space of $U(N)$ gauge-invariant operators in coupled matrix-vector systems at finite $N$, extending previous work on single matrix models. By using the Molien-Weyl formula, we compute the partition function and identify…
We investigated the phase diagram of $SU(3)$ gauge theory in four dimension with one compact dimension by using the perturbative one-loop effective potential. Effects of the adjoint and fundamental fermions are investigated and then the…
The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it…
Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…