Boundary field induced first-order transition in the 2D Ising model: numerical study

In a recent paper, Clusel and Fortin [J. Phys. A.: Math. Gen. 39 (2006) 995] presented an analytical study of a first-order transition induced by an inhomogeneous boundary magnetic field in the two-dimensional Ising model. They identified the transition that separates the regime where the interface is localized near the boundary from the one where it is propagating inside the bulk. Inspired by these results, we measured the interface tension by using multimagnetic simulations combined with parallel tempering to determine the phase transition and the location of the interface. Our results are in very good agreement with the theoretical predictions. Furthermore, we studied the spin-spin correlation function for which no analytical results are available.Comment: 12 pages, 7 figures, 2 table

Resolution among major placental mammal interordinal relationships with genome data imply that speciation influenced their earliest radiations

Background: A number of the deeper divergences in the placental mammal tree are still inconclusively resolved despite extensive phylogenomic analyses. A recent analysis of 200 kbp of protein coding sequences yielded only limited support for the relationships among Laurasiatheria (cow, dog, bat and shrew), probably because the divergences occurred only within a few million years from each other. It is generally expected that increasing the amount of data and improving the taxon sampling enhance the resolution of narrow divergences. Therefore these and other difficult splits were examined by phylogenomic analysis of the hitherto largest sequence alignment. The increasingly complete genome data of placental mammals also allowed developing a novel and stringent data search method. Results: The rigorous data handling, recursive BLAST, successfully removed the sequences from gene families, including those from well-known families hemoglobin, olfactory, myosin and HOX genes, thus avoiding alignment of possibly paralogous sequences. The current phylogenomic analysis of 3,012 genes (2,844,615 nucleotides) from a total of 22 species yielded statistically significant support for most relationships. While some major clades were confirmed using genomic sequence data, the placement of the treeshrew, bat and the relationship between Boreoeutheria, Xenarthra and Afrotheria remained problematic to resolve despite the size of the alignment. Phylogenomic analysis of divergence times dated the basal placental mammal splits at 95–100 million years ago. Many of the following divergences occurred only a few (2–4) million years later. Relationships with narrow divergence time intervals received unexpectedly limited support even from the phylogenomic analyses. Conclusion: The narrow temporal window within which some placental divergences took place suggests that inconsistencies and limited resolution of the mammalian tree may have their natural explanation in speciation processes such as lineage sorting, introgression from species hybridization or hybrid speciation. These processes obscure phylogenetic analysis, making some parts of the tree difficult to resolve even with genome data

Spacetime Approach to Phase Transitions

In these notes, the application of Feynman's sum-over-paths approach to thermal phase transitions is discussed. The paradigm of such a spacetime approach to critical phenomena is provided by the high-temperature expansion of spin models. This expansion, known as the hopping expansion in the context of lattice field theory, yields a geometric description of the phase transition in these models, with the thermal critical exponents being determined by the fractal structure of the high-temperature graphs. The graphs percolate at the thermal critical point and can be studied using purely geometrical observables known from percolation theory. Besides the phase transition in spin models and in the closely related $\phi^4$ theory, other transitions discussed from this perspective include Bose-Einstein condensation, and the transitions in the Higgs model and the pure U(1) gauge theory.Comment: 59 pages, 18 figures. Write-up of Ising Lectures presented at the National Academy of Sciences, Lviv, Ukraine, 2004. 2nd version: corrected typo

Fluctuation Pressure of a Stack of Membranes

We calculate the universal pressure constants of a stack of N membranes between walls by strong-coupling theory. The results are in very good agreement with values from Monte-Carlo simulations.Comment: Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of paper also at http://www.physik.fu-berlin.de/~kleinert/31

Monte Carlo study of the evaporation/condensation transition on different Ising lattices

In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous proof for the behavior of the 2D Ising lattice gas, at a finite volume and a fixed excess \delta M of particles (spins) above the ambient gas density (spontaneous magnetisation). By identifying a dimensionless parameter \Delta (\delta M) and a universal constant \Delta_c, they showed in the limit of large system sizes that for \Delta < \Delta_c the excess is absorbed in the background (``evaporated'' system), while for \Delta > \Delta_c a droplet of the dense phase occurs (``condensed'' system). To check the applicability of the analytical results to much smaller, practically accessible system sizes, we performed several Monte Carlo simulations for the 2D Ising model with nearest-neighbour couplings on a square lattice at fixed magnetisation M. Thereby, we measured the largest minority droplet, corresponding to the condensed phase, at various system sizes (L=40, >..., 640). With analytic values for for the spontaneous magnetisation m_0, the susceptibility \chi and the Wulff interfacial free energy density \tau_W for the infinite system, we were able to determine \lambda numerically in very good agreement with the theoretical prediction. Furthermore, we did simulations for the spin-1/2 Ising model on a triangular lattice and with next-nearest-neighbour couplings on a square lattice. Again, finding a very good agreement with the analytic formula, we demonstrate the universal aspects of the theory with respect to the underlying lattice. For the case of the next-nearest-neighbour model, where \tau_W is unknown analytically, we present different methods to obtain it numerically by fitting to the distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl

Re-examining the directional-ordering transition in the compass model with screw-periodic boundary conditions

We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster algorithm in one-dimensional subspaces of the configuration space. This improvement allows us to study classical systems up to $L=512$. Based on the new algorithm we give evidence for the presence of strongly anomalous scaling for periodic boundary conditions which is much worse than anticipated before. We propose and study alternative boundary conditions for the compass model which do not make use of extended configuration spaces and show that they completely remove the problem with finite-size scaling. In the last part, we apply these boundary conditions to the quantum problem and present a considerably improved estimate for the critical temperature which should be of interest for future studies on the compass model. Our investigation identifies a strong one-dimensional magnetic ordering tendency with a large correlation length as the cause of the unusual scaling and moreover allows for a precise quantification of the anomalous length scale involved.Comment: 10 pages, 8 figures; version as publishe