Related papers: Geometrical properties of parafermionic spin model…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
Dimensionality is a critical factor in determining the properties of solids and is an apparent built-in character of the crystal structure. However, it can be an emergent and tunable property in geometrically frustrated spin systems. Here,…
The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim…
The size distribution of geometrical spin clusters is exactly found for the one dimensional Ising model of finite extent. For the values of lattice constant $\beta$ above some "critical value" $\beta_c$ the found size distribution…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
Making use of a recent complete calculation of a chiral six-point correlation function C(z) in a rectangle we calculate various quantities of interest for percolation (SLE parameter \kappa = 6) and many other two-dimensional critical…
We investigate the possibility to construct extended parafermionic conformal algebras whose generating current has spin $1+\frac{1}{K}$, generalizing the superconformal (spin 3/2) and the Fateev Zamolodchikov (spin 4/3) algebras. Models…
In finite-size scaling analyses of critical phenomena, proper consideration of correction terms, which can come from different sources, plays an important role. For the Fortuin-Kasteleyn representation of the $Q$-state Potts model in two…
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
We use scale invariant scattering theory to exactly determine the renormalization group fixed points of a $q$-state Potts model coupled to an $r$-state Potts model in two dimensions. For integer values of $q$ and $r$ the fixed point…
The $s_{i}={1/2}$ nearest neighbor antiferromagnetic Heisenberg model is considered for spins sitting on the vertices of clusters with the connectivity of fullerene molecules and a number of sites $n$ ranging from 24 to 32. Using the…
Stability and diversity are two key properties that living entities share with spin glasses, where they are manifested through the breaking of the phase space into many valleys or local minima connected by saddle points. The topology of the…
A family of $\mathbb Z_n$-symmetric non-Hermitian models of Baxter was shown by Fendley to be exactly solvable via a parafermionic generalization of the Clifford algebra. We study these models with spatially random couplings, and obtain…
The magnetically ordered, low temperature phase of Ising ferro- magnets is manifested within the associated Fortuin-Kasteleyn (FK) random cluster representation by the occurrence of a single positive density percolating cluster. In this…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
We consider a critical Fortuin-Kasteleyn (FK) percolation with cluster weight $q \in [1,4)$ in the plane, and color its clusters in red (respectively blue) with probability $r \in (0,1)$ (respectively $1-r$), independently of each other. We…
We prove convergence of multiple interfaces in the critical planar q = 2 random cluster model, and provide an explicit description of the scaling limit. Remarkably, the expression for the partition function of the resulting multiple…
We propose actions for non-linear sigma models on cosets $G/H$ in 2+1 dimensions that include the most general non-linear realizations of Chern-Simons terms. When $G$ is simply connected and $H$ contains $r$ commuting U(1) factors, there…
The topological defects of Spin($n+1$) nematics in two spatial dimensions, known as disclinations, are characterized by the $\pi_1(\mathbb{R}P^n) = \textrm{Z}_2$ homotopy group for $n\ge2$. We argue that incompressible quantum liquids of…
Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern--Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal non-abelian gauge fields. The gauge algebras consist of Lorentz-tensorial…