Coexistence of excited states in confined Ising systems

Using the density-matrix renormalization-group method we study the two-dimensional Ising model in strip geometry. This renormalization scheme enables us to consider the system up to the size 300 x infinity and study the influence of the bulk magnetic field on the system at full range of temperature. We have found out the crossover in the behavior of the correlation length on the line of coexistence of the excited states. A detailed study of scaling of this line is performed. Our numerical results support and specify previous conclusions by Abraham, Parry, and Upton based on the related bubble model.Comment: 4 Pages RevTeX and 4 PostScript figures included; the paper has been rewritten without including new result

Fixed Point of the Finite System DMRG

The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system algorithm, that uses the block structure B**B. This is because the tensors are not improved directly. We overcome this problem by using the simpler block structure B*B for the final several sweeps in the finite iteration process. It is possible to increase the numerical precision of the finite system algorithm without increasing the computational effort.Comment: 6 pages, 4 figure

Pair contact process with diffusion - A new type of nonequilibrium critical behavior?

Recently Carlon et. al. investigated the critical behavior of the pair contact process with diffusion [cond-mat/9912347]. Using density matrix renormalization group methods, they estimate the critical exponents, raising the possibility that the transition might belong to the same universality class as branching annihilating random walks with even numbers of offspring. This is surprising since the model does not have an explicit parity-conserving symmetry. In order to understand this contradiction, we estimate the critical exponents by Monte Carlo simulations. The results suggest that the transition might belong to a different universality class that has not been investigated before.Comment: RevTeX, 3 pages, 2 eps figures, adapted to final version of cond-mat/991234

Stability domains of actin genes and genomic evolution

In eukaryotic genes the protein coding sequence is split into several fragments, the exons, separated by non-coding DNA stretches, the introns. Prokaryotes do not have introns in their genome. We report the calculations of stability domains of actin genes for various organisms in the animal, plant and fungi kingdoms. Actin genes have been chosen because they have been highly conserved during evolution. In these genes all introns were removed so as to mimic ancient genes at the time of the early eukaryotic development, i.e. before introns insertion. Common stability boundaries are found in evolutionary distant organisms, which implies that these boundaries date from the early origin of eukaryotes. In general boundaries correspond with introns positions of vertebrates and other animals actins, but not much for plants and fungi. The sharpest boundary is found in a locus where fungi, algae and animals have introns in positions separated by one nucleotide only, which identifies a hot-spot for insertion. These results suggest that some introns may have been incorporated into the genomes through a thermodynamic driven mechanism, in agreement with previous observations on human genes. They also suggest a different mechanism for introns insertion in plants and animals.Comment: 9 Pages, 7 figures. Phys. Rev. E in pres

Exons, introns and DNA thermodynamics

The genes of eukaryotes are characterized by protein coding fragments, the exons, interrupted by introns, i.e. stretches of DNA which do not carry any useful information for the protein synthesis. We have analyzed the melting behavior of randomly selected human cDNA sequences obtained from the genomic DNA by removing all introns. A clear correspondence is observed between exons and melting domains. This finding may provide new insights in the physical mechanisms underlying the evolution of genes.Comment: 4 pages, 8 figures - Final version as published. See also Phys. Rev. Focus 15, story 1

Nonequilibrium effects in DNA microarrays: a multiplatform study

It has recently been shown that in some DNA microarrays the time needed to reach thermal equilibrium may largely exceed the typical experimental time, which is about 15h in standard protocols (Hooyberghs et al. Phys. Rev. E 81, 012901 (2010)). In this paper we discuss how this breakdown of thermodynamic equilibrium could be detected in microarray experiments without resorting to real time hybridization data, which are difficult to implement in standard experimental conditions. The method is based on the analysis of the distribution of fluorescence intensities I from different spots for probes carrying base mismatches. In thermal equilibrium and at sufficiently low concentrations, log I is expected to be linearly related to the hybridization free energy $\Delta G$ with a slope equal to $1/RT_{exp}$, where $T_{exp}$ is the experimental temperature and R is the gas constant. The breakdown of equilibrium results in the deviation from this law. A model for hybridization kinetics explaining the observed experimental behavior is discussed, the so-called 3-state model. It predicts that deviations from equilibrium yield a proportionality of $\log I$ to $\Delta G/RT_{eff}$. Here, $T_{eff}$ is an effective temperature, higher than the experimental one. This behavior is indeed observed in some experiments on Agilent arrays. We analyze experimental data from two other microarray platforms and discuss, on the basis of the results, the attainment of equilibrium in these cases. Interestingly, the same 3-state model predicts a (dynamical) saturation of the signal at values below the expected one at equilibrium.Comment: 27 pages, 9 figures, 1 tabl

The Density Matrix Renormalization Group technique with periodic boundary conditions

The Density Matrix Renormalization Group (DMRG) method with periodic boundary conditions is introduced for two dimensional classical spin models. It is shown that this method is more suitable for derivation of the properties of infinite 2D systems than the DMRG with open boundary conditions despite the latter describes much better strips of finite width. For calculation at criticality, phenomenological renormalization at finite strips is used together with a criterion for optimum strip width for a given order of approximation. For this width the critical temperature of 2D Ising model is estimated with seven-digit accuracy for not too large order of approximation. Similar precision is reached for critical indices. These results exceed the accuracy of similar calculations for DMRG with open boundary conditions by several orders of magnitude.Comment: REVTeX format contains 8 pages and 6 figures, submitted to Phys. Rev.

The Mystery of Two Straight Lines in Bacterial Genome Statistics. Release 2007

In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy. The main challenge now is to explain the observed high accuracy. The new phenomenon of complementary symmetry for codon position--specific nucleotide frequencies is observed. The results of analysis of several codon usage models are presented. We demonstrate that the mean--field approximation, which is also known as context--free, or complete independence model, or Segre variety, can serve as a reasonable approximation to the real codon usage. The first two principal components of codon usage correlate strongly with genomic G+C content and the optimal growth temperature respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. First three eigenvalues in codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and archaeal genomes codon usage is clearly distributed along two third order curves with genomic G+C content as a parameter.Comment: Significantly extended version with new data for all the 348 distinct bacterial genomes available in Genbank in April 200

One-dimensional Nonequilibrium Kinetic Ising Models with local spin-symmetry breaking: N-component branching annihilation transition at zero branching rate

The effects of locally broken spin symmetry are investigated in one dimensional nonequilibrium kinetic Ising systems via computer simulations and cluster mean field calculations. Besides a line of directed percolation transitions, a line of transitions belonging to N-component, two-offspring branching annihilating random-walk class (N-BARW2) is revealed in the phase diagram at zero branching rate. In this way a spin model for N-BARW2 transitions is proposed for the first time.Comment: 6 pages, 5 figures included, 2 new tables added, to appear in PR

Incommensurate structures studied by a modified Density Matrix Renormalization Group Method

A modified density matrix renormalization group (DMRG) method is introduced and applied to classical two-dimensional models: the anisotropic triangular nearest- neighbor Ising (ATNNI) model and the anisotropic triangular next-nearest-neighbor Ising (ANNNI) model. Phase diagrams of both models have complex structures and exhibit incommensurate phases. It was found that the incommensurate phase completely separates the disordered phase from one of the commensurate phases, i. e. the non-existence of the Lifshitz point in phase diagrams of both models was confirmed.Comment: 14 pages, 14 figures included in text, LaTeX2e, submitted to PRB, presented at MECO'24 1999 (Wittenberg, Germany