arXiv subjects
Publications and source records attributed to C. -E. Pfister.
One proves the equivalence of a Gibbs measure and a Gibbs conformal measure for a dynamical system (G,X) when G is a countably infinite discrete group acting expansively on a compact ultrametric space X. As an application one proves for any beta-shift, that the unique equilibrium measure for a function of summable variation is a Gibbs measure.
We give a necessary and sufficient condition on beta of the natural extension of a beta-shift, so that any equilibrium measure for a function of bounded total oscillations is a weak Gibbs measure.
For a large class of irreducible shift spaces $X\subset\tA^{\Z^d}$, with $\tA$ a finite alphabet, and for absolutely summable potentials $Φ$, we prove that equilibrium measures for $Φ$ are weak Gibbs measures. In particular, for $d=1$, the result holds for irreducible sofic shifts.
Interface free energy is the contribution to the free energy of a system due to the presence of an interface separating two coexisting phases at equilibrium. It is also called surface tension. The content of the paper is 1) the definition of the interface free energy from first principles of statistical mechanics; 2) a detailed exposition of its basic properties. We consider lattice models with short range interactions, like the Ising model. A nice feature of lattice models is that the interface free energy is anisotropic so that some results are pertinent to the case of a crystal in equilibrium with its vapor. The results of section 2 hold in full generality.
We consider the map $T_{α,β}(x):= βx + α\mod 1$, which admits a unique probability measure of maximal entropy $μ_{α,β}$. For $x \in [0,1]$, we show that the orbit of $x$ is $μ_{α,β}$-normal for almost all $(α,β)\in[0,1)\times(1,\infty)$ (Lebesgue measure). Nevertheless we construct analytic curves in $[0,1)\times(1,\infty)$ along them the orbit of $x=0$ is at most at one point $μ_{α,β}$-normal. These curves are disjoint and they fill the set $[0,1)\times(1,\infty)$. We also study the generalized $β$-maps (in particular the tent map). We show that the critical orbit $x=1$ is normal with respect to the measure of maximal entropy for almost all $β$.
We study the analyticity properties of the free energy $f_\ga(m)$ of the Kac model at points of first order phase transition, in the van der Waals limit $\ga\searrow 0$. We show that there exists an inverse temperature $β_0$ and $\ga_0>0$ such that for all $β\geq β_0$ and for all $\ga\in(0,\ga_0)$, $f_\ga(m)$ has no analytic continuation along the path $m\searrow m^*$ ($m^*$ denotes spontaneous magnetization). The proof consists in studying high order derivatives of the pressure $p_\ga(h)$, which is related to the free energy $f_\ga(m)$ by a Legendre transform.
We review recent results concerning the exponential behaviour of transition probabilities across a gap in the adiabatic limit of the time-dependent Schrödinger equation. They range from an exponential estimate in quite general situations to asymptotic Landau-Zener type formulae for finite dimensional systems, or systems reducible to this case.
We show that a class of spin models, containing the Ashkin-Teller model, admits a generalized random-cluster (GRC) representation. Moreover we show that basic properties of the usual representation, such as FKG inequalities and comparison inequalities, still hold for this generalized random-cluster model. Some elementary consequences are given. We also consider the duality transformations in the spin representation and in the GRC model and show that they commute.
We apply new techniques developed in a previous paper to the study of some surface effects in the 2D Ising model. We examine in particular the pinning-depinning transition. The results are valid for all subcritical temperatures. By duality we obtained new finite size effects on the asymptotic behaviour of the two-point correlation function above the critical temperature. The key-point of the analysis is to obtain good concentration properties of the measure defined on the random lines giving the high-temperature representation of the two-point correlation function, as a consequence of the sharp triangle inequality: let tau(x) be the surface tension of an interface perpendicular to x; then for any x,y tau(x)+tau(y)-tau(x+y) >= 1/kappa(||x||+||y||-||x+y||), where kappa is the maximum curvature of the Wulff shape and ||x|| the Euclidean norm of x.