Related papers: Universality Class of $O(N)$ Models

For the two dimensional randomly disordered three-state Potts ferromagnet, we find numerically that the critical exponent $\eta$ unchanges with the degree of disorder while those of the correlation length ($\nu$) and magnetic susceptibility…

We investigate the three-dimensional O(2) model on lattices of size 8^3 to 160^3 close to the critical point at zero magnetic field. We confirm explicitly the value of the critical coupling J_c found by Ballesteros et al. and estimate there…

We present direct representations of the scaling functions of the 3d O(4) model which are relevant for comparisons to other models, in particular QCD. This is done in terms of expansions in the scaling variable z=t/h^{1/\beta\delta}. The…

The behaviour of the renormalized spin 2-point function in the O(3) and dodecahedron spin model are investigated numerically. The Monte Carlo data show excellent agreement between the two models. The short distance behavior comes very close…

The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is…

The three-dimensional abelian Higgs model has been argued to be dual to a scalar field theory with a global U(1) symmetry. We show that this duality, together with the scaling and universality hypotheses, implies a scaling law for the…

By using the results of a high-statistics (O(10^7) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on large enough…

Numerically we simulate the short-time behaviour of the critical dynamics for the two dimensional Ising model and Potts model with an initial state of very high temperature and small magnetization. Critical initial increase of the…

I provide evidence that the 2D $RP^{N-1}$ model for $N \ge 3$ is equivalent to the $O(N)$-invariant non-linear $\sigma$-model in the continuum limit. To this end, I mainly study particular versions of the models, to be called constraint…

The three-dimensional classical O($N$) model with a boundary has received renewed interest due to the discovery of the extraordinary-log boundary universality class for $2\leq N< N_c$. The critical value $N_c$ and the exponent of the…

Simulation data are analyzed for four 3D spin-$1/2$ Ising models: on the FCC lattice, the BCC lattice, the SC lattice and the Diamond lattice. The observables studied are the susceptibility, the reduced second moment correlation length, and…

We derive direct representations of the scaling functions of the 3d O(4) model which are relevant for comparisons to other models, in particular QCD. This is done in terms of expansions in the scaling variable z= t/h^{1/Delta}. The…

We improve the theoretical estimates of the critical exponents for the three-dimensional XY universality class. We find alpha=-0.0146(8), gamma=1.3177(5), nu=0.67155(27), eta=0.0380(4), beta=0.3485(2), and delta=4.780(2). We observe a…

We study the critical behavior at the ordinary surface universality class of the three-dimensional O($N$) model, bounded by a two-dimensional surface. Using high-precision Monte Carlo simulations of an improved lattice model, where the…

For the three-dimensional random Ising model, the effective sextic coupling constant v_6 and the nonlinear susceptibilities of the fourth (chi_4) and sixth (chi_6) orders are calculated at criticality. These quantities are shown to differ…

We study the Anderson transition in the SU(2) model and the Ando model. We report a new precise estimate of the critical exponent for the symplectic universality class of the Anderson transition. We also report numerical estimation of the…

We construct the general O(N)-symmetric non-linear sigma model in 2+1 spacetime dimensions at the Lifshitz point with dynamical critical exponent z=2. For a particular choice of the free parameters, the model is asymptotically free with the…

Scale-invariant avalanches -- with events of all sizes following power-law distributions -- are considered critical. Above the upper critical dimension of four, the mean-field solution with a robust $3/2$ size exponent describes the…

Classical XY spins on a two dimensional triangular lattice with antiferromagnetic interactions are reconsidered. We find that the Kosterlitz-Thouless transition associated to the U(1) symmetry appears at a temperature 0.0020(2) below the…

An action with $n$ parameters, which generalizes the $O(N) - R P^{N-1}$ -model, is considered in one dimension for general $N$. We use asymptotic expansion techniques to determine where the model becomes critical and show that for the…