Related papers: Gonihedric Ising Actions
We investigate a generalized Ising action containing nearest neighbour, next to nearest neighbour and plaquette terms that has been suggested as a potential string worldsheet discretization on cubic lattices by Savvidy and Wegner. We use…
We investigate a 3d Ising action which corresponds to a a class of models defined by Savvidy and Wegner, originally intended as discrete versions of string theories on cubic lattices. These models have vanishing bare surface tension and the…
Three-dimensional Ising model with the plaquette-type (next-nearest-neighbor and four-spin) interactions is investigated numerically. This extended Ising model, the so-called gonihedric model, was introduced by Savvidy and Wegner as a…
Using a combinatorial method, the partition functions for two-dimensional nearest neighbour Ising models have been derived for a square lattice of 16 sites in the presence of the magnetic field. A novel hierarchical method of enumeration of…
The critical and multicritical behavior of the simple cubic Ising model with nearest-neighbor, next-nearest-neighbor and plaquette interactions is studied using the cube and star-cube approximations of the cluster variation method and the…
Particle and string actions on coset spaces typically lack a quadratic kinetic term, making their quantization difficult. We define a notion of twistors on these spaces, which are hypersurfaces in a vector space that transform linearly…
We investigate three Ising models on the simple cubic lattice by means of Monte Carlo methods and finite-size scaling. These models are the spin-1/2 Ising model with nearest-neighbor interactions, a spin-1/2 model with nearest-neighbor and…
We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the…
It is known that the normal three-dimensional (3D) Ising model on a cubic lattice is dual to the Wegner's 3D $Z_2$ lattice gauge theory. Here we find an unusual $Z_2$ lattice gauge theory which is dual to the 3D Ising model with not only…
The zero-field partition function of two-dimensional nearest neighbor Ising models of square lattices is derived in terms of the generalized hypergeometric series by evaluating the integral in the exact solution of Onsager. An approximate…
The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls…
We investigate as a member of the Ising universality class the Next-Nearest Neighbour Ising model without external field on a simple cubic lattice by using the Monte Carlo Metropolis Algorithm. The Binder cumulant and the susceptibility…
At first we introduce an action for the string, which leads to a worldsheet that always is curved. For this action we study the Poincar\'e symmetry and the associated conserved currents. Then, a generalization of the above action, which…
We have found that the Regge gravity \cite{regge,sorkin}, can be represented as a $superposition$ of less complicated theory of random surfaces with $Euler~character$ as an action. This extends to Regge gravity our previous result…
We consider in this note a class of two-dimensional determinantal Coulomb gases confined by a radial external field. As the number of particles tends to infinity, their empirical distribution tends to a probability measure supported in a…
We use the cluster variation method (CVM) and Monte Carlo simulations to investigate the phase structure of the 3d gonihedric Ising actions defined by Savvidy and Wegner. This model corresponds to the usual three-dimensional cubic Ising…
We generalize the technique of linked cluster expansions on hypercubic lattices to actions that couple fields at lattice sites which are not nearest neighbours. We show that in this case the graphical expansion can be arranged in such a way…
Finite-range interacting spin models are the simplest models to study the effect of beyond nearest-neighbour interactions and access new effects caused by the range of the interactions. Recent experiments have reached the regime of dominant…
We study the globalization of partial actions on sets and topological spaces and of partial coactions on algebras by applying the general theory of globalization for geometric partial comodules, as previously developed by the authors. We…
Kinetic Ising models on the square lattice with both nearest-neighbor interactions and self-interaction are studied for the cases of random sequential updating and parallel updating. The equilibrium phase diagrams and critical dynamics are…