107 research outputs found

### Models of DNA denaturation dynamics: universal properties

We briefly review some of the models used to describe DNA denaturation
dynamics, focusing on the value of the dynamical exponent $z$, which governs
the scaling of the characteristic time $\tau\sim L^z$ as a function of the
sequence length $L$. The models contain different degrees of simplifications,
in particular sometimes they do not include a description for helical
entanglement: we discuss how this aspect influences the value of $z$, which
ranges from $z=0$ to $z \approx 3.3$. Connections with experiments are also
mentioned

### Critical point shift in a fluid confined between opposing walls

The properties of a fluid, or Ising magnet, confined in a $L \times \infty$
geometry with opposing surface fields at the walls are studied by density
matrix renormalization techniques. In particular we focus on the effect of
gravity on the system, which is modeled by a bulk field whose strength varies
linearly with the distance from the walls. It is well known that in the absence
of gravity phase coexistence is restricted to temperatures below the wetting
temperature. We find that gravity restores phase coexistence up to the bulk
critical temperature, in agreement with previous mean field results. A detailed
study of the scaling to the critical point, as $L \to \infty$, is performed.
The temperature shift scales as $1/L^{y_T}$, while the gravitational constant
scales as $1/L^{1+y_H}$, with $y_T$ and $y_H$ the bulk thermal and magnetic
exponents respectively. For weak surface fields and $L$ not too large, we also
observe a regime where the gravitational constant scales as $1/L^{1+y_H -
\Delta_1 y_T}$ ($\Delta_1$ is the surface gap exponent) with a crossover, for
sufficiently large $L$, to a scaling of type $1/L^{1+y_H}$.Comment: 9 pages, RevTeX, 11 PostScript figures included. Minor corrections.
Final version as publishe

### Density Matrix Renormalization Group and Reaction-Diffusion Processes

The density matrix renormalization group (DMRG) is applied to some
one-dimensional reaction-diffusion models in the vicinity of and at their
critical point. The stochastic time evolution for these models is given in
terms of a non-symmetric ``quantum Hamiltonian'', which is diagonalized using
the DMRG method for open chains of moderate lengths (up to about 60 sites). The
numerical diagonalization methods for non-symmetric matrices are reviewed.
Different choices for an appropriate density matrix in the non-symmetric DMRG
are discussed. Accurate estimates of the steady-state critical points and
exponents can then be found from finite-size scaling through standard
finite-lattice extrapolation methods. This is exemplified by studying the
leading relaxation time and the density profiles of diffusion-annihilation and
of a branching-fusing model in the directed percolation universality class.Comment: 16 pages, latex, 5 PostScript figures include

### A Transfer Matrix study of the staggered BCSOS model

The phase diagram of the staggered six vertex, or body centered solid on
solid model, is investigated by transfer matrix and finite size scaling
techniques. The phase diagram contains a critical region, bounded by a
Kosterlitz-Thouless line, and a second order line describing a deconstruction
transition. In part of the phase diagram the deconstruction line and the
Kosterlitz-Thouless line approach each other without merging, while the
deconstruction changes its critical behaviour from Ising-like to a different
universality class. Our model has the same type of symmetries as some other
two-dimensional models, such as the fully frustrated XY model, and may be
important for understanding their phase behaviour. The thermal behaviour for
weak staggering is intricate. It may be relevant for the description of
surfaces of ionic crystals of CsCl structure.Comment: 13 pages, RevTex, 1 Postscript file with all figures, to be published
in Phys. Rev.

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