402 research outputs found
Relaxation of Surface Profiles by Evaporation Dynamics
We present simulations of the relaxation towards equilibrium of one
dimensional steps and sinusoidal grooves imprinted on a surface below its
roughening transition. We use a generalization of the hypercube stacking model
of Forrest and Tang, that allows for temperature dependent
next-nearest-neighbor interactions. For the step geometry the results at T=0
agree well with the t^(1/4) prediction of continuum theory for the spreading of
the step. In the case of periodic profiles we modify the mobility for the tips
of the profile and find the approximate solution of the resulting free boundary
problem to be in reasonable agreement with the T=0 simulations.Comment: 6 pages, Revtex, 5 Postscript figures, to appear in PRB 15, October
199
Boundary critical behaviour of two-dimensional random Ising models
Using Monte Carlo techniques and a star-triangle transformation, Ising models
with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on
a square lattice with a (1,1) surface are studied near the phase transition.
Both surface and bulk critical properties are investigated. In particular, the
critical exponents of the surface magnetization, 'beta_1', of the correlation
length, 'nu', and of the critical surface correlations, 'eta_{\parallel}', are
analysed.Comment: 16 pages in ioplppt style, 7 ps figures, submitted to J. Phys.
Interfacial adsorption phenomena of the three-dimensional three-state Potts model
We study the interfacial adsorption phenomena of the three-state
ferromagnetic Potts model on the simple cubic lattice by the Monte Carlo
method. Finite-size scaling analyses of the net-adsorption yield the evidence
of the phase transition being of first-order and .Comment: 14 page
Quantum Monte Carlo scheme for frustrated Heisenberg antiferromagnets
When one tries to simulate quantum spin systems by the Monte Carlo method,
often the 'minus-sign problem' is encountered. In such a case, an application
of probabilistic methods is not possible. In this paper the method has been
proposed how to avoid the minus sign problem for certain class of frustrated
Heisenberg models. The systems where this method is applicable are, for
instance, the pyrochlore lattice and the Heisenberg model. The method
works in singlet sector. It relies on expression of wave functions in dimer
(pseudo)basis and writing down the Hamiltonian as a sum over plaquettes. In
such a formulation, matrix elements of the exponent of Hamiltonian are
positive.Comment: 19 LaTeX pages, 6 figures, 1 tabl
Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition
Monte Carlo simulations and finite-size scaling analysis have been carried
out to study the critical behavior and universality for the isotropic-nematic
phase transition in a system of long straight rigid rods of length
(-mers) on two-dimensional lattices. The nematic phase, characterized by a
big domain of parallel -mers, is separated from the isotropic state by a
continuous transition occurring at a finite density. The determination of the
critical exponents, along with the behavior of Binder cumulants, indicate that
the transition belongs to the 2D Ising universality class for square lattices
and the three-state Potts universality class for triangular lattices.Comment: 7 pages, 8 figures, uses epl2.cls, to appear in Europhysics Letter
Droplets in the coexistence region of the two-dimensional Ising model
The two-dimensional Ising model with fixed magnetization is studied using
Monte Carlo techniques. At the coexistence line, the macroscopic, extensive
droplet of minority spins becomes thermally unstable by breaking up into
microscopic clusters. Intriguing finite--size effects as well as singularities
of thermal and cluster properties associated with the transition are discussed.Comment: 7 pages, 3 figures included, submitted to J. Phys. A: Math. Ge
Lifshitz points in blends of AB and BC diblock copolymers
We consider micro- and macro-phase separation in blends of AB and BC flexible diblock copolymers. We show that, depending on architecture, a number of phase diagram topologies are possible. Microphase separation or macrophase separation can occur, and there are a variety of possible Lifshitz points. Because of the rich parameter space, Lifshitz points of multiple order are possible. We demonstrate Lifshitz points of first and second order, and argue that, in principle, up to 5th-order Lifshitz points are possible
Surface critical behavior of two-dimensional dilute Ising models
Ising models with nearest-neighbor ferromagnetic random couplings on a square
lattice with a (1,1) surface are studied, using Monte Carlo techniques and
star-tiangle transformation method. In particular, the critical exponent of the
surface magnetization is found to be close to that of the perfect model,
beta_s=1/2. The crossover from surface to bulk critical properties is
discussed.Comment: 6 pages in RevTex, 3 ps figures, to appear in Journal of Stat. Phy
Critical, crossover, and correction-to-scaling exponents for isotropic Lifshitz points to order
A two-loop renormalization group analysis of the critical behaviour at an
isotropic Lifshitz point is presented. Using dimensional regularization and
minimal subtraction of poles, we obtain the expansions of the critical
exponents and , the crossover exponent , as well as the
(related) wave-vector exponent , and the correction-to-scaling
exponent to second order in . These are compared with
the authors' recent -expansion results [{\it Phys. Rev. B} {\bf 62}
(2000) 12338; {\it Nucl. Phys. B} {\bf 612} (2001) 340] for the general case of
an -axial Lifshitz point. It is shown that the expansions obtained here by a
direct calculation for the isotropic () Lifshitz point all follow from the
latter upon setting . This is so despite recent claims to the
contrary by de Albuquerque and Leite [{\it J. Phys. A} {\bf 35} (2002) 1807].Comment: 11 pages, Latex, uses iop stylefiles, some graphs are generated
automatically via texdra
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