87 research outputs found
Ordering of geometrically frustrated classical and quantum Ising magnets
A systematic study of both classical and quantum geometric frustrated Ising
models with a competing ordering mechanism is reported in this paper. The
ordering comes in the classical case from a coupling of 2D layers and in the
quantum model from the quantum dynamics induced by a transverse field. By
mapping the Ising models on a triangular lattice to elastic lattices of
non-crossing strings, we derive an exact relation between the spin variables
and the displacement field of the strings. Using this map both for the
classical (2+1)D stacked model and the quantum frustrated 2D system, we obtain
a microscopic derivation of an effective Hamiltonian which was proposed before
on phenomenological grounds within a Landau-Ginzburg-Wilson approach. In
contrast to the latter approach, our derivation provides the coupling constants
and hence the entire transverse field--versus--temperature phase diagram can be
deduced, including the universality classes of both the quantum and the
finite--temperature transitions. The structure of the ordered phase is obtained
from a detailed entropy argument. We compare our predictions to recent
simulations of the quantum system and find good agreement. We also analyze the
connections to a dimer model on the hexagonal lattice and its height profile
representation, providing a simple derivation of the continuum free energy and
a physical explanation for the universality of the stiffness of the height
profile for anisotropic couplings.Comment: 15 pages, 7 figure
Disorder Driven Roughening Transitions of Elastic Manifolds and Periodic Elastic Media
The simultaneous effect of both disorder and crystal-lattice pinning on the
equilibrium behavior of oriented elastic objects is studied using scaling
arguments and a functional renormalization group technique. Our analysis
applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic
media, e.g., charge-density waves or flux-line lattices. The competition
between both pinning mechanisms leads to a continuous, disorder driven
roughening transition between a flat state where the mean relative displacement
saturates on large scales and a rough state with diverging relative
displacement. The transition can be approached by changing the impurity
concentration or, indirectly, by tuning the temperature since the pinning
strengths of the random and crystal potential have in general a different
temperature dependence. For D dimensional elastic manifolds interacting with
either random-field or random-bond disorder a transition exists for 2<D<4, and
the critical exponents are obtained to lowest order in \epsilon=4-D. At the
transition, the manifolds show a superuniversal logarithmic roughness. Dipolar
interactions render lattice effects relevant also in the physical case of D=2.
For periodic elastic media, a roughening transition exists only if the ratio p
of the periodicities of the medium and the crystal lattice exceeds the critical
value p_c=6/\pi\sqrt{\epsilon}. For p<p_c the medium is always flat. Critical
exponents are calculated in a double expansion in \mu=p^2/p_c^2-1 and
\epsilon=4-D and fulfill the scaling relations of random field models.Comment: 23 pages, 9 figure
Critical Casimir Force between Inhomogeneous Boundaries
To study the critical Casimir force between chemically structured boundaries
immersed in a binary mixture at its demixing transition, we consider a strip of
Ising spins subject to alternating fixed spin boundary conditions. The system
exhibits a boundary induced phase transition as function of the relative amount
of up and down boundary spins. This transition is associated with a sign change
of the asymptotic force and a diverging correlation length that sets the scale
for the crossover between different universal force amplitudes. Using conformal
field theory and a mapping to Majorana fermions, we obtain the universal
scaling function of this crossover, and the force at short distances.Comment: 5 pages, 3 figure
Casimir--Polder force between anisotropic nanoparticles and gently curved surfaces
The Casimir--Polder interaction between an anisotropic particle and a surface
is orientation dependent. We study novel orientational effects that arise due
to curvature of the surface for distances much smaller than the radii of
curvature by employing a derivative expansion. For nanoparticles we derive a
general short distance expansion of the interaction potential in terms of their
dipolar polarizabilities. Explicit results are presented for nano-spheroids
made of SiO and gold, both at zero and at finite temperatures. The
preferred orientation of the particle is strongly dependent on curvature,
temperature, as well as material properties.Comment: 9 pages, 10 encapsulated figure
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