Finite-size scaling study of the three-dimensional classical Heisenberg model

Finite - Size Scaling Study of the Three - Dimensional Classical Heisenberg Model ∗

We use the single-cluster Monte Carlo update algorithm to simulate the three-dimensional classical Heisenberg model in the critical region on simple cubic lattices of size L3 with L = 12, 16, 20, 24, 32, 40, and 48. By means of finite-size scaling analyses we compute high-precision estimates of the critical temperature and the critical exponents, using extensively histogram reweighting and opti...

Finite Size Scaling in Three-Dimensional Bootstrap Percolation

Finite size scaling in three-dimensional bootstrap percolation

We consider the problem of bootstrap percolation on a three dimensional lattice and we study its finite size scaling behavior. Bootstrap percolation is an example of Cellular Automata defined on the d-dimensional lattice {1, 2, ..., L} in which each site can be empty or occupied by a single particle; in the starting configuration each site is occupied with probability p, occupied sites remain o...

Finite - size scaling study of the equilibrium cluster distribution of the two - dimensional Ising model

We use a very fast and efficient algorithm to study by Monte Carlo methods the equilibrium cluster distribution C,(L) , the mean number of clusters per lattice site containing I particles in a square lattice of L2 sites, of the two-dimensional fsing model at the critical point. Finite-size scaling theory is then used to analyse the scalingansatz C,(L) = [-If(2'/L), T and s being critical expone...

Universal amplitude ratios in finite-size scaling: three-dimensional Ising model

Motivated by the results of two-dimensional conformal field theory (CFT) we investigate the finite-size scaling of the mass spectrum of an Ising model on three-dimensional lattices with a spherical cross section. Using a cluster-update Monte Carlo technique we find a linear relation between the masses and the corresponding scaling dimensions, in complete analogy to the situation in two dimensio...