Related papers: Spin interfaces and crossing probabilities of spin…
Scharmm-Loewner evolution (SLE) and conformal field theory (CFT) are popular and widely used instruments to study critical behavior of two-dimensional models, but they use different objects. While SLE has natural connection with lattice…
Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a…
The conformal loop ensemble (CLE) has two phases: for $\kappa \in (8/3, 4]$, the loops are simple and do not touch each other or the boundary; for $\kappa \in (4,8)$, the loops are non-simple and may touch each other and the boundary. For…
We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in…
We provide a pedagogical review of CFT techniques to compute certain Schramm-Loewner Evolution (SLE) observables in the upper half-plane. The approach relies on the ability to express the observables as bulk-boundary correlation functions…
We address the geometrical critical behavior of the two-dimensional Q-state Potts model in terms of the spin clusters (i.e., connected domains where the spin takes a constant value). These clusters are different from the usual…
The multi-spin coding of the Monte Carlo simulation of the three-state Potts model on the simple cubic lattice is presented. The ferromagnetic (F) model, the antiferromagnetic (AF) model, and the random mixture of the F and AF couplings are…
The magnetic susceptibility and spin-spin correlation of the double-exchange model for doped manganites are investigated through the Monte Carlo calculations on the three-dimensional lattice model. Deviations of the susceptibility from the…
The variational cluster approximation is used to study the ground-state properties and single-particle spectra of the three-component fermionic Hubbard model defined on the two-dimensional square lattice at half filling. First, we show that…
The aim of this paper is to test numerically the predictions of the Mode Coupling Theory (MCT) of the glass transition and study its finite size scaling properties in a model with an exact MCT transition, which we choose to be the fully…
For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N_Gamma of clusters that intersect a given contour Gamma. To leading order, N_Gamma is proportional to…
Starting with the Ising model, statistical models with global symmetries provide fruitful approaches to interesting physical systems, for example percolation or polymers. These include the $O(n)$ model (symmetry group $O(n)$) and the Potts…
Conformally-invariant curves that appear at critical points in two-dimensional statistical mechanics systems, and their fractal geometry have received a lot of attention in recent years. On the one hand, Schramm has invented a new rigorous…
We study the Levin-Wen string-net model with a $Z_N$ type fusion algebra. Solutions of the local constraints of this model correspond to $Z_N$ gauge theory and double Chern-simons theories with quantum groups. For the first time, we…
The Hubbard model at temperatures above the N\'{e}el transition, despite being a paramagnet, can exhibit rich physics due to the interplay of Fermi surface, on-site interaction $U$ and thermal fluctuations. Nevertheless, the understanding…
We construct models hosting classical fractal spin liquids on two realistic three-dimensional (3D) lattices of corner-sharing triangles: trillium and hyperhyperkagome (HHK). Both models involve the same form of three-spin Ising interactions…
We study connection probabilities between vertices of the square lattice for the critical random-cluster (FK) model with cluster weight 2, which is related to the critical Ising model. We consider the model on the plane and on domains…
Theories of anti-commuting scalar fields are non-unitary, but they are of interest both in statistical mechanics and in studies of the higher spin de Sitter/Conformal Field Theory correspondence. We consider an $Sp(N)$ invariant theory of…
We report on Monte Carlo studies of the kinetic exchange model for (III,Mn)V ferromagnetic semiconductors in which S=5/2 local moments, representing Mn^{2+} ions, are exchange coupled to band electrons. We treat the Mn^{2+}$ spin…
Three-dimensional N-vector spin models may define universality classes for such diverse phenomena as i) the superfluid transition in liquid helium (currently investigated in the micro-gravity environment of the Space Shuttle) and ii) the…