Scaling in the vicinity of the four-state Potts fixed point

We study a self-dual generalization of the Baxter-Wu model, employing results obtained by transfer matrix calculations of the magnetic scaling dimension and the free energy. While the pure critical Baxter-Wu model displays the critical behavior of the four-state Potts fixed point in two dimensions, in the sense that logarithmic corrections are absent, the introduction of different couplings in the up- and down triangles moves the model away from this fixed point, so that logarithmic corrections appear. Real couplings move the model into the first-order range, away from the behavior displayed by the nearest-neighbor, four-state Potts model. We also use complex couplings, which bring the model in the opposite direction characterized by the same type of logarithmic corrections as present in the four-state Potts model. Our finite-size analysis confirms in detail the existing renormalization theory describing the immediate vicinity of the four-state Potts fixed point.Comment: 19 pages, 7 figure

Extended surface disorder in the quantum Ising chain

We consider random extended surface perturbations in the transverse field Ising model decaying as a power of the distance from the surface towards a pure bulk system. The decay may be linked either to the evolution of the couplings or to their probabilities. Using scaling arguments, we develop a relevance-irrelevance criterion for such perturbations. We study the probability distribution of the surface magnetization, its average and typical critical behaviour for marginal and relevant perturbations. According to analytical results, the surface magnetization follows a log-normal distribution and both the average and typical critical behaviours are characterized by power-law singularities with continuously varying exponents in the marginal case and essential singularities in the relevant case. For enhanced average local couplings, the transition becomes first order with a nonvanishing critical surface magnetization. This occurs above a positive threshold value of the perturbation amplitude in the marginal case.Comment: 15 pages, 10 figures, Plain TeX. J. Phys. A (accepted

Effective Field Theory of the Zero-Temperature Triangular-Lattice Antiferromagnet: A Monte Carlo Study

Using a Monte Carlo coarse-graining technique introduced by Binder et al., we have explicitly constructed the continuum field theory for the zero-temperature triangular Ising antiferromagnet. We verify the conjecture that this is a gaussian theory of the height variable in the interface representation of the spin model. We also measure the height-height correlation function and deduce the stiffness constant. In addition, we investigate the nature of defect-defect interactions at finite temperatures, and find that the two-dimensional Coulomb gas scenario applies at low temperatures.Comment: 26 pages, 9 figure

Monte Carlo Renormalization of the 3-D Ising model: Analyticity and Convergence

We review the assumptions on which the Monte Carlo renormalization technique is based, in particular the analyticity of the block spin transformations. On this basis, we select an optimized Kadanoff blocking rule in combination with the simulation of a d=3 Ising model with reduced corrections to scaling. This is achieved by including interactions with second and third neighbors. As a consequence of the improved analyticity properties, this Monte Carlo renormalization method yields a fast convergence and a high accuracy. The results for the critical exponents are y_H=2.481(1) and y_T=1.585(3).Comment: RevTeX, 4 PostScript file

Monte Carlo Calculation of Free Energy, Critical Point, and Surface Critical Behavior of Three-Dimensional Heisenberg Ferromagnets

A transfer-matrix Monte Carlo technique is developed to compute the free energy of three-dimensional, classical Heisenberg ferromagnets. From the free energy of systems with periodic and antiperiodic boundary conditions, helicity moduli are calculated. From these the critical couplings for simple-cubic (sc) and face-centered-cubic lattices are estimated by use of finite-size scaling. For the simple-cubic lattice, the critical dimension of the surface magnetization is estimated with standard Monte Carlo methods, yielding a result in excellent agreement with the ε-expansion work of Diehl and Nüsser

Geometric properties of two-dimensional O(n) loop configurations

We study the fractal geometry of O($n$) loop configurations in two dimensions by means of scaling and a Monte Carlo method, and compare the results with predictions based on the Coulomb gas technique. The Monte Carlo algorithm is applicable to models with noninteger $n$ and uses local updates. Although these updates typically lead to nonlocal modifications of loop connectivities, the number of operations required per update is only of order one. The Monte Carlo algorithm is applied to the O($n$) model for several values of $n$, including noninteger ones. We thus determine scaling exponents that describe the fractal nature of O($n$) loops at criticality. The results of the numerical analysis agree with the theoretical predictions.Comment: 18 pages, 6 figure