RESUMO
We study the probability distribution P(M) of the order parameter (average magnetization) M, for the finite-size systems at the critical point. The systems under consideration are the 3-dimensional Ising model on a simple cubic lattice, and its 3-state generalization known to have remarkably small corrections to scaling. Both models are studied in a cubic box with periodic boundary conditions. The model with reduced corrections to scaling makes it possible to determine P(M) with unprecedented precision. We also obtain a simple, but remarkably accurate, approximate formula describing the universal shape of P(M).
RESUMO
We study the three-dimensional Ising model at the critical point in the fixed-magnetization ensemble, by means of the recently developed geometric cluster Monte Carlo algorithm. We define a magnetic-field-like quantity in terms of microscopic spin-up and spin-down probabilities in a given configuration of neighbors. In the thermodynamic limit, the relation between this field and the magnetization reduces to the canonical relation M(h). However, for finite systems, the relation is different. We establish a close connection between this relation and the probability distribution of the magnetization of a finite-size system in the canonical ensemble.
RESUMO
We determine the phase diagram of the O(n) loop model on the honeycomb lattice, in particular, in the range n>2, by means of a transfer-matrix method. We find that, contrary to the prevailing expectation, there is a line of critical points in the range between n = 2 and infinity. This phase transition, which belongs to the three-state Potts universality class, is unphysical in terms of the O(n) spin model, but falls inside the physical region of the n-component corner-cubic model. It can also be interpreted in terms of the ordering of a system of soft particles with hexagonal symmetry.