相关论文: Conformal invariance in random cluster models. I. …
For a four dimensional, unitary, diffeomorphism- and scale invariant quantum field theory without higher derivatives and a well defined scale current we argue that scale invariance implies conformal invariance. The proof relies on the…
We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a…
We study various mathematical aspects of discrete models on graphs, specifically the Dimer and the Ising models. We focus on proving gluing formulas for individual summands of the partition function. We also obtain partial results regarding…
We provide a concise exposition with original proofs of combinatorial formulas for the 2D Ising model partition function, multi-point fermionic observables, spin and energy density correlations, for general graphs and interaction constants,…
The application of machine learning models can be significantly impeded by the occurrence of distributional shifts, as the assumption of homogeneity between the population of training and testing samples in machine learning and statistics…
We study fermionic conformal field theories on surfaces with spin structure in the presence of boundaries, defects, and interfaces. We obtain the relevant crossing relations, taking particular care with parity signs and signs arising from…
The frequency-dependent scaling of the dispersive and dissipative parts of the alternating susceptibility is studied for spin glasses at criticality. An extension of the usual $\omega t$-scaling is proposed. Simulational data from the…
We consider the critical behavior of two-dimensional layered Ising models where the exchange couplings between neighboring layers follow hierarchical sequences. The perturbation caused by the non-periodicity could be irrelevant, relevant or…
We formulate the conformal mapping between $R^3$ and $S^3$, the 3 sphere. This mapping is applied to the critical Ising model. From this mapping, we calculate the second and fourth moments of the magnetization density, and using those…
In recent years there has been a lot of interest in discussing frame dependences/independences of the cosmological perturbations under the conformal transformations. This problem has previously been investigated in terms of the covariant…
We discuss a geometrical interpretation of the Z-invariant Ising model in terms of isoradial embeddings of planar lattices. The Z-invariant Ising model can be defined on an arbitrary planar lattice if and only if certain paths on the…
Conformal symmetry underlies the mathematical description of various two-dimensional integrable models (e.g. for their Lax representation, Poisson algebra, zero curvature representation,...) or of conformal models (for the anomalous Ward…
In critical lattice models, distance ($r$) dependent correlation functions contain power laws $r^{-2\Delta}$ governed by scaling dimensions $\Delta$ of an underlying continuum field theory. In Monte Carlo simulations, the leading dimensions…
We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a fermionic observable and compute its scaling limit by discrete…
The morphological nature of structures that form under gravitational instability has been of central interest to cosmology for over two decades. A remarkable feature of large scale structures in the Universe is that they occupy a relatively…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
We present a search for conformal invariance in vorticity isolines of two-dimensional compressible turbulence. The vorticity is measured by tracking the motion of particles that float at the surface of a turbulent tank of water. The…
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,…
The dimer model is the study of random dimer covers (perfect matchings) of a graph. A double-dimer configuration on a graph $G$ is a union of two dimer covers of $G$. We introduce quaternion weights in the dimer model and show how they can…
We study the finite-size scaling of the free energy of the Ising model on lattices with the topology of the tetrahedron and the octahedron. Our construction allows to perform changes in the length scale of the model without altering the…