Related papers: Conformal Invariance in the Long-Range Ising Model
The critical behavior of Ising model on a one-dimensional network, which has long-range connections at distances $l>1$ with the probability $\Theta(l)\sim l^{-m}$, is studied by using Monte Carlo simulations. Through studying the Ising…
Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent theta or a dynamical exponent z. For a given value of theta, we construct local scale transformations which can…
The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the…
In a recent paper (arXiv:0906.3219) the representation of Nekrasov partition function in terms of nontrivial two-dimensional conformal field theory has been suggested. For non-vanishing value of the deformation parameter…
The concept of conformal field theory provides a general classification of statistical systems on two-dimensional geometries at the point of a continuous phase transition. Considering the finite-size scaling of certain special observables,…
Observation of the cosmic microwave background is consistent with the $R^2$ model. In the $R^2$ model, there exists a dimensionless constant which must be assigned a very large value to reconcile the model with the data. We show that the…
We consider the Ising model on the square lattice with biaxially correlated random ferromagnetic couplings, the critical point of which is fixed by self-duality. The disorder represents a relevant perturbation according to the extended…
We argue that the local violation of P invariance in heavy ion collisions is a consequence of the long range topological order which is inherent feature of strongly coupled QCD. A similar phenomenon is known to occur in some topologically…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
Scaling limits of critical percolation models show major differences between low and high dimensional models. The article discusses the formulation of the continuum limit for the former case. A mathematical framework is proposed for the…
Recently-developed variational perturbation expansions converge exponentially fast for positive coupling constants. They do not, however, possess the correct left-hand cut in the complex coupling constant plane, implying a wrong large-order…
We study the second-moment correlation length and the reduced susceptibility of two ferromagnetic Ising models with zero-temperature ordering. By introducing a scaling variable motivated by high-temperature series expansions, we are able to…
The fractal structure and scaling properties of a 2d slice of the 3d Ising model is studied using Monte Carlo techniques. The percolation transition of geometric spin (GS) clusters is found to occur at the Curie point, reflecting the…
We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling…
We investigate a non solvable two-dimensional ferromagnetic Ising model with nearest neighbor plus weak finite range interactions of strength \lambda. We rigorously establish one of the predictions of Conformal Field Theory (CFT), namely…
We study Ising chains with arbitrary multispin finite-range couplings, providing an explicit solution of the associated inverse Ising problem, i.e. the problem of inferring the values of the coupling constants from the correlation…
A process that images or measures bond energies in the critical Ising model can be in distinct measurement ``phases'', depending on the precision of measurement. We study the transition into the strong-measurement phase using replica field…
In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor…
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
Abelian gauge theory in $d\neq 4$ spacetime dimensions is an example of a scale invariant theory which does not possess conformal symmetry -- the special conformal transformation(SCT) explicitly breaks the gauge invariance of the theory. In…