Related papers: Spin state sum models in two dimensions
I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension.
We introduce a new classical spin liquid on the pyrochlore lattice by extending spin ice with further neighbour interactions. We find that this disorder free spin model exhibits a form of dynamical heterogeneity with extremely slow…
We give a short review of the spin foam models of quantum gravity, with an emphasis on the Barret-Crane model. After explaining the shortcomings of the Barret-Crane model, we briefly discuss two new approaches, one based on the 3d spin foam…
Method of derivation of the duality relations for two-dimensional Z(N)-symmetric spin models on finite square lattice wrapped on the torus is proposed. As example, exact duality relations for the nonhomogeneous Ising model (N=2) and the…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and…
The gonihedric spin model was first introduced as the action for a discretized tensionless string in a discretized embeding space. Afterwards was found that there are interesting features on the dynamical behavior of this model in 3…
This paper is a follow-up to a previous paper on fermions. A simple state sum model for a scalar field on a triangulated 1-manifold is constructed. The model is independent of the triangulation and gives exactly the same partition function…
We apply the time-dependent local-spin-density approximation as general theory to describe ground states and spin-density oscillations in the linear response regime of two-dimensional nanostructures of arbitrary shape. For this purpose, a…
The notion of the spin is shown to have two constituents, as exemplified by the spin of the electron. The first one is related to the form of the wave equation and determines the fermion or boson particle type. This implies the spin taking…
Loop quantum gravity has provided us with a canonical framework especially devised for background independent and diffeomorphism invariant gauge field theories. In this quantization the fundamental excitations are called spin network…
We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…
The aim of the present article is to study in detail the so-called spin equation (SE) and present both the methods of generating new solution and a new set of exact solutions. We recall that the SE with a real external field can be treated…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
The nontrivial topology of spin systems such as skyrmions in real space can promote complex electronic states. Here, we provide a general viewpoint at the emergence of topological electronic states in spin systems based on the methods of…
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…
A construction supporting a conjecture that different ground state pairs exist in the 2-dimensional Edwards-Anderson Ising spin glass is presented.
Solvable vertex models in two dimensions are of importance in conformal field theory, phase transitions and integrable models. We consider here the $D_n$ spin vertex models, for $n$ which is odd. The models involve also the anti--spinor…
We consider spin systems between a finite number $N$ of "species" or "phases" partitioning a cubic lattice $\mathbb{Z}^d$. We suppose that interactions between points of the same phase are coercive, while between point of different phases…
The nature of equilibrium states in disordered materials is often studied using an overlap function P(q), the probability of two configurations having similarity q. Exact sampling simulations of a two-dimensional proxy for three-dimensional…