33 research outputs found
Roughening Induced Deconstruction in (100) Facets of CsCl Type Crystals
The staggered 6-vertex model describes the competition between surface
roughening and reconstruction in (100) facets of CsCl type crystals. Its phase
diagram does not have the expected generic structure, due to the presence of a
fully-packed loop-gas line. We prove that the reconstruction and roughening
transitions cannot cross nor merge with this loop-gas line if these degrees of
freedom interact weakly. However, our numerical finite size scaling analysis
shows that the two critical lines merge along the loop-gas line, with strong
coupling scaling properties. The central charge is much larger than 1.5 and
roughening takes place at a surface roughness much larger than the conventional
universal value. It seems that additional fluctuations become critical
simultaneously.Comment: 31 pages, 9 figure
Renormalization group trajectories from resonance factorized S-matrices
We propose and investigate a large class of models possessing resonance
factorized S-matrices. The associated Casimir energy describes a rich pattern
of renormalization group trajectories related to flows in the coset models
based on the simply laced Lie Algebras. From a simplest resonance S-matrix,
satisfying the ``-property'', we predict new flows in non-unitary
minimal models.Comment: (7 pages) (no figures included
Local functional models of critical correlations in thin-films
Recent work on local functional theories of critical inhomogeneous fluids and
Ising-like magnets has shown them to be a potentially exact, or near exact,
description of universal finite-size effects associated with the excess
free-energy and scaling of one-point functions in critical thin films. This
approach is extended to predict the two-point correlation function G in
critical thin-films with symmetric surface fields in arbitrary dimension d. In
d=2 we show there is exact agreement with the predictions of conformal
invariance for the complete spectrum of correlation lengths as well as the
detailed position dependence of the asymptotic decay of G. In d=3 and d>=4 we
present new numerical predictions for the universal finite-size correlation
length and scaling functions determining the structure of G across the
thin-film. Highly accurate analytical closed form expressions for these
universal properties are derived in arbitrary dimension.Comment: 4 pages, 1 postscript figure. Submitted to Phys Rev Let
Monte Carlo study of the Widom-Rowlinson fluid using cluster methods
The Widom-Rowlinson model of a fluid mixture is studied using a new cluster
algorithm that is a generalization of the invaded cluster algorithm previously
applied to Potts models. Our estimate of the critical exponents for the
two-component fluid are consistent with the Ising universality class in two and
three dimensions. We also present results for the three-component fluid.Comment: 13 pages RevTex and 2 Postscript figure
A model with simultaneous first and second order phase transitions
We introduce a two dimensional nonlinear XY model with a second order phase
transition driven by spin waves, together with a first order phase transition
in the bond variables between two bond ordered phases, one with local
ferromagnetic order and another with local antiferromagnetic order. We also
prove that at the transition temperature the bond-ordered phases coexist with a
disordered phase as predicted by Domany, Schick and Swendsen. This last result
generalizes the result of Shlosman and van Enter (cond-mat/0205455). We argue
that these phenomena are quite general and should occur for a large class of
potentials.Comment: 7 pages, 7 figures using pstricks and pst-coi
Thermodynamics and Topology of Disordered Systems: Statistics of the Random Knot Diagrams on Finite Lattice
The statistical properties of random lattice knots, the topology of which is
determined by the algebraic topological Jones-Kauffman invariants was studied
by analytical and numerical methods. The Kauffman polynomial invariant of a
random knot diagram was represented by a partition function of the Potts model
with a random configuration of ferro- and antiferromagnetic bonds, which
allowed the probability distribution of the random dense knots on a flat square
lattice over topological classes to be studied. A topological class is
characterized by the highest power of the Kauffman polynomial invariant and
interpreted as the free energy of a q-component Potts spin system for
q->infinity. It is shown that the highest power of the Kauffman invariant is
correlated with the minimum energy of the corresponding Potts spin system. The
probability of the lattice knot distribution over topological classes was
studied by the method of transfer matrices, depending on the type of local
junctions and the size of the flat knot diagram. The obtained results are
compared to the probability distribution of the minimum energy of a Potts
system with random ferro- and antiferromagnetic bonds.Comment: 37 pages, latex-revtex (new version: misprints removed, references
added
From Tomonaga-Luttinger to Fermi liquid in transport through a tunneling barrier
Finite length of a one channel wire results in crossover from a
Tomonaga-Luttinger to Fermi liquid behavior with lowering energy scale. In
condition that voltage drop mostly occurs across a tunnel barrier inside
the wire we found coefficients of temperature/voltage expansion of low energy
conductance as a function of constant of interaction, right and left traversal
times. At higher voltage the finite length contribution exhibits oscillations
related to both traversal times and becomes a slowly decaying correction to the
scale-invariant dependence of the conductance.Comment: 12 pages of RevTex file and 1 PS file figur
Metal-insulator transition in the one-dimensional SU(N) Hubbard model
We investigate the metal-insulator transition of the one-dimensional SU(N)
Hubbard model for repulsive interaction. Using the bosonization approach a Mott
transition in the charge sector at half-filling (k_F=\pi/Na_0) is conjectured
for N > 2. Expressions for the charge and spin velocities as well as for the
Luttinger liquid parameters and some correlation functions are given. The
theoretical predictions are compared with numerical results obtained with an
improved zero-temperature quantum Monte Carlo approach. The method used is a
generalized Green's function Monte Carlo scheme in which the stochastic time
evolution is partially integrated out. Very accurate results for the gaps,
velocities, and Luttinger liquid parameters as a function of the Coulomb
interaction U are given for the cases N=3 and N=4. Our results strongly support
the existence of a Mott-Hubbard transition at a {\it non-zero} value of the
Coulomb interaction. We find for N=3 and for N=4.Comment: 22 pages, 9 Fig
Ising Universality in Three Dimensions: A Monte Carlo Study
We investigate three Ising models on the simple cubic lattice by means of
Monte Carlo methods and finite-size scaling. These models are the spin-1/2
Ising model with nearest-neighbor interactions, a spin-1/2 model with
nearest-neighbor and third-neighbor interactions, and a spin-1 model with
nearest-neighbor interactions. The results are in accurate agreement with the
hypothesis of universality. Analysis of the finite-size scaling behavior
reveals corrections beyond those caused by the leading irrelevant scaling
field. We find that the correction-to-scaling amplitudes are strongly dependent
on the introduction of further-neighbor interactions or a third spin state. In
a spin-1 Ising model, these corrections appear to be very small. This is very
helpful for the determination of the universal constants of the Ising model.
The renormalization exponents of the Ising model are determined as y_t = 1.587
(2), y_h = 2.4815 (15) and y_i = -0.82 (6). The universal ratio Q =
^2/ is equal to 0.6233 (4) for periodic systems with cubic symmetry.
The critical point of the nearest-neighbor spin-1/2 model is K_c=0.2216546
(10).Comment: 25 pages, uuencoded compressed PostScript file (to appear in Journal
of Physics A