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For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…

Dynamical Systems · Mathematics 2023-05-31 Charlene Kalle , Benthen Zeegers

We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite…

Statistical Mechanics · Physics 2009-03-28 Benjamin Hsu , Michael Mulligan , Eduardo Fradkin , Eun-Ah Kim

We investigate the percolative properties of the vacant set left by random interlacements on Z^d, when d is large. A non-negative parameter u controls the density of random interlacements on Z^d. It is known from arXiv:0704.2560, and…

Probability · Mathematics 2011-09-01 Alain-Sol Sznitman

We prove quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Z^d, d>=2, with long-range correlations introduced in arXiv:1212.2885, solving one of the…

Probability · Mathematics 2015-09-28 Eviatar Procaccia , Ron Rosenthal , Artem Sapozhnikov

We investigate the role of relaxation mechanisms in the driven response of elastic disordered interfaces in finite dimensions, focusing on the interplay between dimensionality and interaction range. Through extensive numerical simulations,…

Disordered Systems and Neural Networks · Physics 2025-08-14 Giuseppe Petrillo , Eduardo Jagla , Eugenio Lippiello , Alberto Rosso

This is a detailed analysis of invariant measures for one-dimensional dynamical systems with random switching. In particular, we prove smoothness of the invariant densities away from critical points and describe the asymptotics of the…

Dynamical Systems · Mathematics 2015-10-28 Yuri Bakhtin , Tobias Hurth , Jonathan C. Mattingly

We study the nonequilibrium phase transition in the two-dimensional contact process on a randomly diluted lattice by means of large-scale Monte-Carlo simulations for times up to $10^{10}$ and system sizes up to $8000 \times 8000$ sites. Our…

Disordered Systems and Neural Networks · Physics 2009-01-13 Thomas Vojta , Adam Farquhar , Jason Mast

The two-dimensional (2D) random-bond Ising model has a novel multicritical point on the ferromagnetic to paramagnetic phase boundary. This random phase transition is one of the simplest examples of a 2D critical point occurring at both…

Statistical Mechanics · Physics 2009-10-28 Sora Cho , Matthew P. A. Fisher

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in…

Disordered Systems and Neural Networks · Physics 2023-11-10 Aidan Zabalo , Justin H. Wilson , Michael J. Gullans , Romain Vasseur , Sarang Gopalakrishnan , David A. Huse , J. H. Pixley

We investigate entanglement measures in the infinite-dimensional regime. First, we discuss the peculiarities that may occur if the Hilbert space of a bi-partite system is infinite-dimensional, most notably the fact that the set of states…

Quantum Physics · Physics 2009-11-07 Jens Eisert , Christoph Simon , Martin B. Plenio

The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…

Mathematical Physics · Physics 2007-05-23 Michael Aizenman

We study the classical dimer model on a square lattice with a single vacancy by developing a graph-theoretic classification of the set of all configurations which extends the spanning tree formulation of close-packed dimers. With this…

Statistical Mechanics · Physics 2007-10-31 J. Bouttier , M. Bowick , E. Guitter , M. Jeng

For a random walk on the integer lattice $\mathbb{Z}$ that is attracted to a strictly stable process with index $\alpha\in (1, 2)$ we obtain the asymptotic form of the transition probability for the walk killed when it hits a finite set.…

Probability · Mathematics 2019-04-24 Kohei Uchiyama

A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state…

High Energy Physics - Lattice · Physics 2010-11-19 Carl M. Bender , Peter N. Meisinger , Stefan Boettcher

We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on $Z^d \times Z_+$. In dimensions $d>6$, we obtain bounds on exit times, transition probabilities, and the range of the…

Probability · Mathematics 2007-09-01 Martin T. Barlow , Antal A. Jarai , Takashi Kumagai , Gordon Slade

Recurrence quantification analysis is a method for measuring the complexity of dynamical systems. Recurrence determinism is a fundamental characteristic of it, closely related to correlation sum. In this paper, we study asymptotic behavior…

Dynamical Systems · Mathematics 2023-04-05 Michaela Mihoková

We examine the ground state of the random quantum Ising model in a transverse field using a generalization of the Ma-Dasgupta-Hu renormalization group (RG) scheme. For spatial dimensionality d=2, we find that at strong randomness the RG…

Disordered Systems and Neural Networks · Physics 2009-10-31 Olexei Motrunich , Siun-Chuon Mau , David A. Huse , Daniel S. Fisher

We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…

High Energy Physics - Lattice · Physics 2009-10-22 I. Campos , A. Tarancon

In this article, we first extend the construction of random interlacements, introduced by A.S. Sznitman in [arXiv:0704.2560], to the more general setting of transient weighted graphs. We prove the Harris-FKG inequality for this model and…

Probability · Mathematics 2009-07-03 Augusto Teixeira

We prove the uniqueness of the infinite connected component for the vacant set of random interlacements on general vertex-transitive amenable transient graphs. Our approach is based on connectedness of random interlacements and differs from…

Probability · Mathematics 2024-12-23 Yingxin Mu , Artem Sapozhnikov