316 research outputs found
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
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
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
Geometric properties of two-dimensional O(n) loop configurations
We study the fractal geometry of O() 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 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() model for several values of , including
noninteger ones. We thus determine scaling exponents that describe the fractal
nature of O() loops at criticality. The results of the numerical analysis
agree with the theoretical predictions.Comment: 18 pages, 6 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
Finite-size scaling and conformal anomaly of the Ising model in curved space
We study the finite-size scaling of the free energy of the Ising model on
lattices with the topology of the tetrahedron and the octahedron. Our
construction allows to perform changes in the length scale of the model without
altering the distribution of the curvature in the space. We show that the
subleading contribution to the free energy follows a logarithmic dependence, in
agreement with the conformal field theory prediction. The conformal anomaly is
given by the sum of the contributions computed at each of the conical
singularities of the space, except when perfect order of the spins is precluded
by frustration in the model.Comment: 4 pages, 4 Postscript figure
Surface Critical Behavior of Binary Alloys and Antiferromagnets: Dependence of the Universality Class on Surface Orientation
The surface critical behavior of semi-infinite
(a) binary alloys with a continuous order-disorder transition and
(b) Ising antiferromagnets in the presence of a magnetic field is considered.
In contrast to ferromagnets, the surface universality class of these systems
depends on the orientation of the surface with respect to the crystal axes.
There is ordinary and extraordinary surface critical behavior for orientations
that preserve and break the two-sublattice symmetry, respectively. This is
confirmed by transfer-matrix calculations for the two-dimensional
antiferromagnet and other evidence.Comment: Final version that appeared in PRL, some minor stylistic changes and
one corrected formula; 4 pp., twocolumn, REVTeX, 3 eps fig
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