Surface transitions of the semi-infinite Potts model I: the high bulk temperature regime

We propose a rigorous approach of Semi-Infinite lattice systems illustrated with the study of surface transitions of the semi-infinite Potts model

Surface transitions of the semi-infinite Potts model II: the low bulk temperature regime

We consider the semi-infinite (q)-state Potts model. We prove, for large (q), the existence of a first order surface phase transition between the ordered phase and the the so-called "new low temperature phase" predicted in \cite{Li}, in which the bulk is ordered whereas the surface is disordered

Euler-Poincare' Characteristic and Phase Transition in the Potts Model

Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. This approach provides an alternative way of inspecting the critical behaviour of random systems in statistical mechanics. For the 2d q-states Potts model with q <= 6, intensive and accurate numerics indicates that the average of the Euler characteristic (taken with respect to the Fortuin-Kasteleyn random cluster measure) is an order parameter of the phase transition.Comment: 17 pages, 8 figures, 1 tabl

Interface Tensions and Perfect Wetting in the Two-Dimensional Seven-State Potts Model

We present a numerical determination of the order-disorder interface tension, \sod, for the two-dimensional seven-state Potts model. We find \sod=0.0114\pm0.0012, in good agreement with expectations based on the conjecture of perfect wetting. We take into account systematic effects on the technique of our choice: the histogram method. Our measurements are performed on rectangular lattices, so that the histograms contain identifiable plateaus. The lattice sizes are chosen to be large compared to the physical correlation length. Capillary wave corrections are applied to our measurements on finite systems.Comment: 8 pages, LaTex file, 2 postscript figures appended, HLRZ 63/9

Monovalent Ion Condensation at the Electrified Liquid/Liquid Interface

X-ray reflectivity studies demonstrate the condensation of a monovalent ion at the electrified interface between electrolyte solutions of water and 1,2-dichloroethane. Predictions of the ion distributions by standard Poisson-Boltzmann (Gouy-Chapman) theory are inconsistent with these data at higher applied interfacial electric potentials. Calculations from a Poisson-Boltzmann equation that incorporates a non-monotonic ion-specific potential of mean force are in good agreement with the data.Comment: 4 pages, 4 figure

Complex zero-free regions at large |q| for multivariate Tutte polynomials (alias Potts-model partition functions) with general complex edge weights

We find zero-free regions in the complex plane at large |q| for the multivariate Tutte polynomial (also known in statistical mechanics as the Potts-model partition function) Z_G(q,w) of a graph G with general complex edge weights w = {w_e}. This generalizes a result of Sokal (cond-mat/9904146) that applies only within the complex antiferromagnetic regime |1+w_e| \le 1. Our proof uses the polymer-gas representation of the multivariate Tutte polynomial together with the Penrose identity.Comment: LaTeX2e, 34 pages. Version 2 improves Theorem 1.3, using an improved Proposition 4.4 and a new Proposition 5.2. Version 3 (published in JCTB) makes many improvements: Theorems 1.2 and 1.3 are strengthened; the bounds of Section 5 are generalized to allow vertex weights; the discussion in Section 6 and examples in Section 7 are re-though