Critical exponents and unusual properties of the broken phase in the 3d-RP(2) antiferromagnetic model

We present the results of a Monte Carlo simulation of the antiferromagnetic RP(2) model in three dimensions. With finite-size scaling techniques we accurately measure the critical exponents and compare them with those of O(N) models. We are able to parameterize the corrections-to-scaling. The symmetry properties of the broken phase are also studied.Comment: 4 pages, TeX type, Poster session contribution to "Lattice96" conference, Washington University, StLoui

Spin Glass Ordering in Diluted Magnetic Semiconductors: a Monte Carlo Study

We study the temperature-dilution phase diagram of a site-diluted Heisenberg antiferromagnet on a fcc lattice, with and without the Dzyaloshinskii-Moriya anisotropic term, fixed to realistic microscopic parameters for $IIB_{1-x} Mn_x Te$ (IIB=Cd, Hg, Zn). We show that the dipolar Dzyaloshinskii-Moriya anisotropy induces a finite-temperature phase transition to a spin glass phase, at dilutions larger than 80%. The resulting probability distribution of the order parameter P(q) is similar to the one found in the cubic lattice Edwards-Anderson Ising model. The critical exponents undergo large finite size corrections, but tend to values similar to the ones of the Edwards-Anderson-Ising model.Comment: 4 pages plus 3 postscript figure

Finite Size Scaling and ``perfect'' actions: the three dimensional Ising model

Using Finite-Size Scaling techniques, we numerically show that the first irrelevant operator of the lattice $\lambda\phi^4$ theory in three dimensions is (within errors) completely decoupled at $\lambda=1.0$. This interesting result also holds in the Thermodynamical Limit, where the renormalized coupling constant shows an extraordinary reduction of the scaling-corrections when compared with the Ising model. It is argued that Finite-Size Scaling analysis can be a competitive method for finding improved actions.Comment: 13 pages, 3 figure

The antiferromagnetic phi4 Model, II. The one-loop renormalization

It is shown that the four dimensional antiferromagnetic lattice phi4 model has the usual non-asymptotically free scaling law in the UV regime around the chiral symmetrical critical point. The theory describes a scalar and a pseudoscalar particle. A continuum effective theory is derived for low energies. A possibility of constructing a model with a single chiral boson is mentioned.Comment: To appear in Phys. Rev.

Finite-size scaling study of the d=4 site-diluted Ising

We study the four dimensional site-diluted Ising model using finite-size scaling techniques. We explore the whole parameter space (density-coupling) in order to determine the Universality Class of the transition line. Our data are compatible with Mean Field behavior plus logarithmic corrections.Comment: Contribution to LATTICE 9

The four dimensional site-diluted Ising model: a finite-size scaling study

Using finite-size scaling techniques, we study the critical properties of the site-diluted Ising model in four dimensions. We carry out a high statistics Monte Carlo simulation for several values of the dilution. The results support the perturbative scenario: there is only the Ising fixed point with large logarithmic scaling corrections. We obtain, using the Perturbative Renormalization Group, functional forms for the scaling of several observables that are in agreement with the numerical data.Comment: 30 pages, 8 postscript figure

Universality Class of Thermally Diluted Ising Systems at Criticality

The universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality, is investigated by finite size scaling techniques using the Monte Carlo method. We find that the critical temperature, the critical exponents and therefore the universality class of these thermally diluted Ising systems depart markedly from the ones of short range correlated disordered systems. Our results agree fairly well with theoretical predictions previously made by Weinrib and Halperin for systems with long range correlated disorder.Comment: 7 pages, 6 figures, RevTe

Antiferromagnetism in four dimensions: search for non-triviality

We present antiferromagnetism as a mechanism capable of modifying substantially the phase diagram and the critical behaviour of statistical mechanical models. This is particularly relevant in four dimensions, due to the connection between second order transition points and the continuum limit as a quantum field theory. We study three models with an antiferromagnetic interaction: the Ising and the O(4) Models with a second neighbour negative coupling, and the \RP{2} Model. Different conclusions are obtained depending on the model.Comment: 4 pages LateX. Contribution to Lat9

Monte Carlo studies of antiferromagnetic spin models in three dimensions

We study several antiferromagnetic formulations of the O(3) spin model in three dimensions by means of Monte Carlo simulations. We discuss about the vacua properties and analyze the phase transitions. Using Finite Size Scaling analysis we conclude that all phase transitions found are of first orderComment: 4 pages, 2 Postscript figures. Contribution to Lattice '9

Critical properties of the Antiferromagnetic \RP2$ model in three dimensions

We study the behavior of the antiferromagnetic RP$^2$ model in $d=3$. The vacuum structure is analyzed in the critical and low temperature regions, paying special attention to the spontaneous symmetry breaking pattern. Near the critical point we observe a full breakdown of the O(3) symmetry of the action. Several methods for computing critical exponents are compared. We conclude that the most solid determination is obtained using a measure of the correlation length. Corrections-to-scaling are parameterized, yielding a very accurate determination of the critical coupling and a 5\% error measure of the related exponent. This is used to estimate the systematic errors due to finite-size effects.Comment: 31 pages, 10 postscript figure