Parallel-tempering cluster algorithm for computer simulations of critical phenomena

In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest, we introduce a flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain one to two orders of magnitude in the performance for 2D and 3D Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.Comment: pages, 5 figures, and 2 table

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

Information Geometry and Phase Transitions

The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A non-interacting model has a flat geometry (R=0), while R diverges at the critical point of an interacting one. Here, the information geometry is studied for a number of solvable statistical-mechanical models.Comment: 6 pages with 1 figur

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

Substrate Adhesion of a Nongrafted Flexible Polymer in a Cavity

In a contact density chain-growth study we investigate the solubility-temperature pseudo-phase diagram of a lattice polymer in a cavity with an attractive surface. In addition to the main phases of adsorbed and desorbed conformations we find numerous subphases of collapsed and expanded structures.Comment: 20 pages, 6 figure