Related papers: Gibbs measures for hardcore-SOS models on Cayley t…
In this note, we give a nature action of the modular group on the ends of the infinite (p + 1)-cayley tree, for each prime p. We show that there is a unique invariant probability measure for each p.
On a finite graph, there is a natural family of Boltzmann probability measures on cycle-rooted spanning forests, parametrized by weights on cycles. For a certain subclass of those weights, we construct Gibbs measures in infinite volume, as…
We present an exact solution of the q-state Potts model on a class of generalized Sierpinski fractal lattices. The model is shown to possess an ordered phase at low temperatures and a continuous transition to the high temperature disordered…
In this paper, we consider the classical Ising model on the Cayley tree of order k and show the existence of the phase transition in the following sense: there exists two quantum Markov states which are not quasi-equivalent. It turns out…
This paper is devoted to the study of Gibbs u-states for the geodesic flow tangent to a foliation with negatively curved leaves. On the one hand we give sufficient conditions for the existence of transverse invariant measures. In particular…
We obtain measure rigidity results for stationary measures of random walks generated by diffeomorphisms, and for actions of $\operatorname{SL}(2,\mathbb{R})$ on smooth manifolds. Our main technical result, from which the rest of the…
In this paper we study Hard-Core model on a Cayley tree. For a normal divisor of index four new conditions for uniqueness and non-uniqueness of weakly periodic Gibbs measures are found.
We consider a branching random walk with binary state space and index set $T^k$, the infinite rooted tree in which each node has k children (also known as the model of "broadcasting on a tree"). The root of the tree takes a random value 0…
We study the nonequilibrium properties of directed Ising models with non conserved dynamics, in which each spin is influenced by only a subset of its nearest neighbours. We treat the following models: (i) the one-dimensional chain; (ii) the…
Absolute transition frequencies of the $2s\; ^2{\rm S}_{1/2} \rightarrow 2p\;^2\mathrm{P}_{1/2,3/2}$ transitions in Be$^+$ were measured for the isotopes $^{7,9-12}$Be. The fine structure splitting of the $2p$ state and its isotope…
We consider general classes of gradient models on regular trees with values in a countable Abelian group $S$ such as $\mathbb{Z}$ or $\mathbb{Z}_q$, in regimes of strong coupling (or low temperature). This includes unbounded spin models…
We provide an existence theory for gradient Gibbs measures for Z-valued spin models on regular trees which are not invariant under translations of the tree, assuming only summability of the transfer operator. The gradient states we obtain…
In this paper we give a short proof that the projection of a Gibbs state for a H\"older continuous potential on a mixing shift of finite type under a 1-block fiber-wise mixing factor map has a H\"older continuous g function. This improves a…
Gibbsian line ensembles are families of Brownian lines arising in many natural contexts such as the level curves of three dimensional Ising interfaces, the solid-on-solid model, multi-layered polynuclear growth etc. An important example is…
Consider a statistical physical model on the $d$-regular infinite tree $T_{d}$ described by a set of interactions $\Phi$. Let $\{G_{n}\}$ be a sequence of finite graphs with vertex sets $V_n$ that locally converge to $T_{d}$. From $\Phi$…
For a fixed topological Markov shift, we consider measure-preserving dynamical systems of Gibbs measures for 2-locally constant functions on the shift. We also consider isomorphisms between two such systems. We study the set of all…
We study, by the Mean Field and Monte Carlo methods, a generalized q-state Potts gonihedric model. The phase transition of the model becomes stronger with increasing $q.$ The value $k_c(q),$ at which the phase transition becomes second…
We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…
An instance of a random constraint satisfaction problem defines a random subset S (the set of solutions) of a large product space (the set of assignments). We consider two prototypical problem ensembles (random k-satisfiability and…
To construct the high-temperature effective field theory of gauge-Higgs models up to $\mathcal{O}(g^6)$ in the gauge coupling, we integrate out hard modes to three-loop level and use the next-to-next-to-leading order effective potential.…