Related papers: Conformal Invariance and SLE in Two-Dimensional Is…
We examine three--dimensional turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-L\"owner evolution curves (SLE). The data stems from a run on a grid of $1536^3$ points, with…
This paper studies the Yang-Lee edge singularity of 2-dimensional (2D) Ising model based on a quantum spin chain and transfer matrix measurements on the cylinder. Based on finite-size scaling, the low-lying excitation spectrum is found at…
This paper reports numerical studies of a compressible version of the Ising spin glass in two dimensions. Compressibility is introduced by adding a term that couples the spin-spin interactions and local lattice deformations to the standard…
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising…
Infinite-range spin-glass models with Levy-distributed interactions show a freezing transition similar to disordered spin systems on finite connectivity random graphs. It is shown that despite diverging moments of the local field…
The Schramm-Loewner evolution (SLE) describes the continuum limit of domain walls at phase transitions in two dimensional statistical systems. We consider here the SLEs in the self-dual Z(N) spin models at the critical point. For N=2 and…
The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction $w$ of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an…
We discuss several problems concerning domain walls in the spin $S$ Ising model at zero temperature in a magnetic field, $H/(2S)$, applied in the $x$ direction. Some results are also given for the planar ($y$-$z$) model in a transverse…
The energy of a droplet of linear extent l in the droplet theory of spin glasses goes as l^{\theta} for large l. It is shown by numerical studies of large droplets in two-dimensional systems that this formula needs to be modified by the…
Given a simply connected planar domain D, distinct points x,y \in \partial D, and \kappa >0, the Schramm-Loewner evolution SLE_\kappa is a random continuous non-self-crossing path in the closure of D from x to y. The…
We investigate the charge and spin structures associated with arbitrary smooth polarization textures in Ising (integer) quantum Hall ferromagnets. We consider the case where the two polarizations (denoted "pseudospin" up and down)…
We derive the Ward identities of Conformal Field Theory (CFT) within the framework of Schramm-Loewner Evolution (SLE) and some related processes. This result, inspired by the observation that particular events of SLE have the correct…
We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a…
Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling…
We investigate magnetic properties of a two-dimensional periodic structure with Ising spins and antiferromagnetic nearest neighbor interaction. The structure is topologically equivalent to the Archimedean (3,12^2) lattice. The ground state…
Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those…
Extensive simulations are made on Ising Spin Glasses (ISG) with Gaussian, Laplacian and bimodal interaction distributions in dimension four. Standard finite size scaling analyses near and at criticality provide estimates of the critical…
We address the question of weak versus strong universality scenarios for the random-bond Ising model in two dimensions. A finite-size scaling theory is proposed, which explicitly incorporates $\ln L$ corrections ($L$ is the linear finite…
It was realized recently that the chordal, radial and dipolar SLEs are special cases of a general slit holomorphic stochastic flow. We characterize those slit holomorphic stochastic flows which generate level lines of the Gaussian free…
Following the approach outlined in [18], convergence to SLE6 of the Exploration Processes for the correlated bond-triangular type models studied in [7] is established. This puts the said models in the same universality class as the standard…