101 research outputs found
Unbiased sampling of globular lattice proteins in three dimensions
We present a Monte Carlo method that allows efficient and unbiased sampling
of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit
each lattice site exactly once. They are often used as simple models of
globular proteins, upon adding suitable local interactions. Our algorithm can
easily be equipped with such interactions, but we study here mainly the
flexible homopolymer case where each conformation is generated with uniform
probability. We argue that the algorithm is ergodic and has dynamical exponent
z=0. We then use it to study polymers of size up to 64^3 = 262144 monomers.
Results are presented for the effective interaction between end points, and the
interaction with the boundaries of the system
Role of conformational entropy in force-induced bio-polymer unfolding
A statistical mechanical description of flexible and semi-flexible polymer
chains in a poor solvent is developed in the constant force and constant
distance ensembles. We predict the existence of many intermediate states at low
temperatures stabilized by the force. A unified response to pulling and
compressing forces has been obtained in the constant distance ensemble. We show
the signature of a cross-over length which increases linearly with the chain
length. Below this cross-over length, the critical force of unfolding decreases
with temperature, while above, it increases with temperature. For stiff chains,
we report for the first time "saw-tooth" like behavior in the force-extension
curves which has been seen earlier in the case of protein unfolding.Comment: 4 pages, 5 figures, ReVTeX4 style. Accepted in Phys. Rev. Let
Exact overlaps in the Kondo problem
It is well known that the ground states of a Fermi liquid with and without a
single Kondo impurity have an overlap which decays as a power law of the system
size, expressing the Anderson orthogonality catastrophe. Ground states with two
different values of the Kondo couplings have, however, a finite overlap in the
thermodynamic limit. This overlap, which plays an important role in quantum
quenches for impurity systems, is a universal function of the ratio of the
corresponding Kondo temperatures, which is not accessible using perturbation
theory nor the Bethe ansatz. Using a strategy based on the integrable structure
of the corresponding quantum field theory, we propose an exact formula for this
overlap, which we check against extensive density matrix renormalization group
calculations.Comment: 4.5+7 pages. 3 figure
Critical interfaces in the random-bond Potts model
We study geometrical properties of interfaces in the random-temperature
q-states Potts model as an example of a conformal field theory weakly perturbed
by quenched disorder. Using conformal perturbation theory in q-2 we compute the
fractal dimension of Fortuin Kasteleyn domain walls. We also compute it
numerically both via the Wolff cluster algorithm for q=3 and via
transfer-matrix evaluations. We obtain numerical results for the fractal
dimension of spin cluster interfaces for q=3. These are found numerically
consistent with the duality kappa(spin) * kappa(FK)= 16 as expressed in
putative SLE parameters.Comment: 4 page
Exact overlaps in the Kondo problem
It is well known that the ground states of a Fermi liquid with and without a
single Kondo impurity have an overlap which decays as a power law of the system
size, expressing the Anderson orthogonality catastrophe. Ground states with two
different values of the Kondo couplings have, however, a finite overlap in the
thermodynamic limit. This overlap, which plays an important role in quantum
quenches for impurity systems, is a universal function of the ratio of the
corresponding Kondo temperatures, which is not accessible using perturbation
theory nor the Bethe ansatz. Using a strategy based on the integrable structure
of the corresponding quantum field theory, we propose an exact formula for this
overlap, which we check against extensive density matrix renormalization group
calculations.Comment: 4.5+7 pages. 3 figure
On the universality of compact polymers
Fully packed loop models on the square and the honeycomb lattice constitute
new classes of critical behaviour, distinct from those of the low-temperature
O(n) model. A simple symmetry argument suggests that such compact phases are
only possible when the underlying lattice is bipartite. Motivated by the hope
of identifying further compact universality classes we therefore study the
fully packed loop model on the square-octagon lattice. Surprisingly, this model
is only critical for loop weights n < 1.88, and its scaling limit coincides
with the dense phase of the O(n) model. For n=2 it is exactly equivalent to the
selfdual 9-state Potts model. These analytical predictions are confirmed by
numerical transfer matrix results. Our conclusions extend to a large class of
bipartite decorated lattices.Comment: 13 pages including 4 figure
Unconventional continuous phase transition in a three dimensional dimer model
Phase transitions occupy a central role in physics, due both to their
experimental ubiquity and their fundamental conceptual importance. The
explanation of universality at phase transitions was the great success of the
theory formulated by Ginzburg and Landau, and extended through the
renormalization group by Wilson. However, recent theoretical suggestions have
challenged this point of view in certain situations. In this Letter we report
the first large-scale simulations of a three-dimensional model proposed to be a
candidate for requiring a description beyond the Landau-Ginzburg-Wilson
framework: we study the phase transition from the dimer crystal to the Coulomb
phase in the cubic dimer model. Our numerical results strongly indicate that
the transition is continuous and are compatible with a tricritical universality
class, at variance with previous proposals.Comment: 4 pages, 3 figures; v2: minor changes, published versio
Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model
The two-dimensional Potts model can be studied either in terms of the
original Q-component spins, or in the geometrical reformulation via
Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for
arbitrary real values of Q by construction, it was only shown very recently
that the spin representation can be promoted to the same level of generality.
In this paper we show how to define the Potts model in terms of observables
that simultaneously keep track of the spin and FK degrees of freedom. This is
first done algebraically in terms of a transfer matrix that couples three
different representations of a partition algebra. Using this, one can study
correlation functions involving any given number of propagating spin clusters
with prescribed colours, each of which contains any given number of distinct FK
clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the
Kac form h_{r,s}, with integer indices r,s that we determine exactly both in
the bulk and in the boundary versions of the problem. In particular, we find
that the set of points where an FK cluster touches the hull of its surrounding
spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains
this set to points where the neighbouring spin cluster extends to infinity, we
show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are
supported by extensive transfer matrix and Monte Carlo computations.Comment: 15 pages, 3 figures, 2 table
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