We obtain the local magnetization of a planar Ising model with defects of different types. It is shown that near the critical point the local magnetization has a nonuniversal behavior that manifests itself in the fact that its critical exponent is a continuous function of the microscopic parameters of the system.
We consider two-dimensional Ising models with randomly distributed ferromagnetic bonds and study the local critical behavior at defect lines by extensive Monte Carlo simulations. Both for ladder and chain type defects, non-universal critical behavior is observed: the critical exponent of the defect magnetization is found to be a continuous function of the strength of the defect coupling. Analyzing corresponding stability conditions, we obtain new evidence that the critical exponent ν of the bulk correlation length of the random Ising model does not depend on dilution, i.e. ν=1.
We discuss the universality classes of the local critical behavior of a bulk system near a free surface and near an internal plane of defects. A phase diagram and plausible renormalization-group flow properties for a general model which encompasses both cases are described qualitatively. Several of the crossover exponents are related to bulk critical exponents or semi-infinite surface critical exponents. The picture which is proposed accomodates systems with nonuniversal local critical exponents near a plane of defects, such as the two-dimensional Ising model near a defect line, in a natural way. Necessary conditions for nonuniversal local critical exponents and for logarithmic corrections are derived. The singularities of the energy densities near a free surface and near an internal defect plane on approaching the bulk critical temperature are analyzed.
We study the behaviour of dynamical critical exponents of the two-dimensional Ising model with a line of defects. Simulations done at an early time (first 100 Monte Carlo steps) reveal that the critical exponent of Janssen et al ( Z. Phys. B 73 539) depends on the strength of the exchange coupling constant of the altered line. On the other hand, our simulations permit us to conclude that the dynamical critical exponent z is not sensitive to changes in . In addition, we investigate the possible invariance of the anomalous dimension of the magnetization at the beginning of the process.
The existence of nonuniversal, as well as surface (universal) critical behavior near a defect plane is demonstrated on a one-dimensional quantum lattice gas model, belonging to the two-dimensional Ising universality class. According to numerical results the weak defect region is attracted by a line of fixed points starting at the bulk critical point, while the strong defect region is controlled by a separate fixed point describing the surface transition of the model. This new kind of phase diagram is argued to be general for two-dimensional lattice gas models.