相关论文: Phase transitions for nonsingular Bernoulli action…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
The main goal of this paper is to give the first examples of equivariant aspherical Poincare complexes, that are not realized by group actions on closed aspherical manifolds $M$. These will also provide new counterexamples to the Nielsen…
We study continuous-time quantum walks on normal Cayley graphs of certain non-abelian groups, called extraspecial groups. By applying general results for graphs in association schemes we determine the precise conditions for perfect state…
Recently Gliozzi has shown that, under certain conditions, it is possible to derive the Dirac-Born-Infeld action for an abelian gauge field of a D-brane. Also, the action turns out to be invariant with respect to a non-linear realization of…
A new type of non-Abelian generalization of the Born-Infeld action is proposed, in which the spacetime indices and group indices are combined. The action is manifestly Lorentz and gauge invariant. In its power expansion, the lowest order…
In this note we show existence of bounded, transitive cocycles over a transitive action of a finitely generated group, and bounded, ergodic cocycles over an ergodic, probability preserving action of $\Bbb Z^d$.
The application of state-of-the-art machine learning techniques to statistical physic problems has seen a surge of interest for their ability to discriminate phases of matter by extracting essential features in the many-body wavefunction or…
We consider the $N$-particle noncolliding Bernoulli random walk --- a discrete time Markov process in $\mathbb{Z}^{N}$ obtained from a collection of $N$ independent simple random walks with steps $\in\{0,1\}$ by conditioning that they never…
We analyze the onset of classical behaviour after a second-order phase transition by considering a scalar field theory in which the system-field interacts with its environment, represented both by further fields and by its own…
Bass-Serre theory provides a powerful framework for studying group actions on trees. While extremely effective for structural questions in group theory, it is less suited to the systematic construction of group actions with prescribed local…
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…
We use partial actions, as formalized by Exel, to construct various commensurating actions. We use this in the context of groups piecewise preserving a geometric structure, and we interpret the transfixing property of these commensurating…
We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
We study the multifractal analysis of a class of self-similar measures with overlaps. This class, for which we obtain explicit formulae for the L^q spectrum tau(q) as well as the singularity spectrum f(alpha), is sufficiently large to point…
Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for…
Consider a group $G$ acting nicely on a simply-connected simplicial complex $X$. Numerous classical methods exist for using this group action to produce a presentation for $G$. For the case that $X/G$ is 2-connected, we give a new method…
We introduce notions of absolutely non-free and perfectly non-free group actions and use them to study the associated unitary representations. We show that every weakly branch group acts absolutely non-freely on the boundary of the…
We prove a new pointwise ergodic theorem for probability-measure-preserving (pmp) actions of free groups, where the ergodic averages are taken over arbitrary finite subtrees of the standard Cayley graph rooted at the identity. This result…
The phase transition in the mean-field XY model is shown analytically to be related to a topological change in its configuration space. Such a topology change is completely described by means of Morse theory allowing a computation of the…