Related papers: Geometry of bounded critical phenomena
We discuss infinitesimal isometries of the middle surfaces and present some characteristic conditions for a function to be the normal component of an infinitesimal isometry. Our results show that those characteristic conditions depend on…
In three dimensions, or more generally, below the upper critical dimension, scaling laws for critical phenomena seem well understood, for both infinite and for finite systems. Above the upper critical dimension of four, finite-size scaling…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
Understanding phase transitions requires not only identifying order parameters but also characterizing how their correlations behave across scales. By quantifying how fluctuations at distinct spatial or temporal points are related,…
We compute the spectral form factor of two integrable quantum-critical many body systems in one spatial dimension. The spectral form factor of the quantum Ising chain is periodic in time in the scaling limit described by a conformal field…
We derived the thermodynamic curvature of the Ising model on a kagome lattice under the presence of an external magnetic field. The curvature was found to have a singularity at the critical point. We focused on the zero field case to derive…
Fractal geometry of random curves appearing in the scaling limit of critical two-dimensional statistical systems is characterized by their harmonic measure and winding angle. The former is the measure of the jaggedness of the curves while…
Critical exponent $\gamma \succeq 1.1$ characterizes behavior of the mechanical susceptibility of a real fluid when temperature approaches the critical one. It results in zero Gaussian curvature of the local shape of the critical point on…
We determine bounds on the curvature of local patches of spacetime from the requirement of intact long-range chiral symmetry. The bounds arise from a scale-dependent analysis of gravitational catalysis and its influence on the effective…
Quantum gravity is investigated in the limit of a large number of space-time dimensions, using as an ultraviolet regularization the simplicial lattice path integral formulation. In the weak field limit the appropriate expansion parameter is…
On a compact Riemannian manifold with boundary, we study the set of conformal metrics of negative constant scalar curvature in the interior and positive constant mean curvature on the boundary. Working in the case of positive Yamabe…
In the ordered phase of the 3D Ising model, minority spin clusters are surrounded by a boundary of dual plaquettes. As the temperature is raised, these spin clusters become more numerous, and it is found that eventually their boundaries…
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…
A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales. Here we define a family of $(2+1)$-dimensional quantum gravity states which arise from curvature excitations…
The fractal structure of high-temperature graphs of the three-dimensional Ising and XY models is investigated by simulating these graphs directly on a cubic lattice and analyzing them with the help of percolation observables. The Ising…
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…
We consider the case with boundary of the classical Kazdan-Warner problem in dimension greater or equal than three, i.e. the prescription of scalar and boundary mean curvatures via conformal deformations of the metric. We deal in particular…
We investigate the low-temperature critical behavior of the three dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature $T \to 0$ the usual scaling relations have to be modified as far as…
While the universe becomes more and more homogeneous at large scales, statistical analysis of galaxy catalogs have revealed a fractal structure at small-scales (\lambda < 100 h^{-1} Mpc), with a fractal dimension D=1.5-2 (Sylos Labini et al…
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…