相关论文: Some Rigorous Results on the Phase Transition of F…

In this paper, we study the evolution of a Finitary Random Interlacement (FRI) with respect to the expected length of each fiber. In contrast to the previously proved phase transition between sufficiently large and small fiber length, we…

In this paper, we prove the exact orders of critical intensity $u_*(T)$ in Finitary Random Interlacements (FRI) in $\mathbb{Z}^d, \ d\ge 3$ with respect to the expected fiber length $T$. We show that as $T\to\infty$, $u_*(T)\sim T^{-1}, \…

We prove that the critical percolation parameter for Finitary Random Interlacements (FRI) is continuous with respect to the path length parameter $T$. The proof uses a result which is interesting on its own right; equality of natural…

We establish sharp asymptotic bounds for the critical intensity of the Finitary Random Interlacements (FRI) model in four and higher dimensions with general trajectory length distributions. Our proof reveals that the construction of…

In this paper, we prove a phase transition in the connectivity of Finitary Random interlacements $\mathcal{FI}^{u,T}$ in $\mathbb{Z}^d$, with respect to the average stopping time. For each $u>0$, with probability one $\mathcal{FI}^{u,T}$…

Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay…

We rigorously analyze the quantum phase transition between a metallic and an insulating phase in (non solvable) interacting spin chains or one dimensional fermionic systems. In particular, we prove the persistence of Luttinger liquid…

We consider a finite Fermi-system where the residual interactions create a soft mode of the excitation spectrum. Because of the large vibrational amplitude, the standard random phase approximation does not work in this situation. We develop…

For a critical simple exchangeable fragmentation-coagulation process in slow regime where the coagulation rate and fragmentation rate are of the same order, we show that there exist phase transitions for its boundary behavior at infinity…

Experimental results obtained at the Relativistic Heavy Ion Collider (RHIC) have been interpreted in terms of a strongly interacting quark gluon plasma. The strongly interacting plasma is characterized by ``perfect fluidity'', i.e. a ratio…

A spatial signal is defined by its evaluations on the whole domain. In this paper, we consider stable reconstruction of real-valued signals with finite rate of innovations (FRI), up to a sign, from their magnitude measurements on the whole…

This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…

We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in $1+1$ space-time dimensions.…

We study the pinning phase transition for discrete surface dynamics in random environments. A renormalization procedure is devised to prove that the interface moves with positive velocity under a finite size condition. This condition is…

A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention…

We study transitions between distinct phases of one-dimensional periodically driven (Floquet) systems. We argue that these are generically controlled by infinite-randomness fixed points of a strong-disorder renormalization group procedure.…

We study an interacting ensemble of instantons at finite baryon chemical potential. We emphasize the importance of fermionic zero modes and calculate the fermion induced interaction between instantons at non-zero chemical potential. We show…

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…

Lifshitz transitions are topological transitions of a Fermi surface, whose signatures typically appear in the conduction properties of a host metal. Here, we demonstrate, using an extended Falicov- Kimball model of a two-flavor fermion…

In these lecture notes we review some recent attempts at searching for non-Fermi liquids and novel quantum phase transitions in holographic systems using gauge/gravity duality. We do this by studying the simplest finite density system…