相关论文: Random Fields, Topology, and The Imry-Ma Argument

We study mean field systems whose free energy landscape is dominated by marginally stable states. We review and develop various techniques to describe such states, elucidating their physical meaning and the interrelation between them. In…

We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural…

We introduce the notion of a random relaxed asymptotic contraction in the setting of random normed modules. The contraction condition employs two quasi-metrics that are built directly from the random operator: a lower quasi-metric which…

We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…

The dominance (preponderance) of the 0+ ground state for random interactions is shown to be a consequence of certain random interactions with chaotic features. These random interactions, called chaotic random interactions, impart a symmetry…

We consider the two-level correlation function in two-dimensional disordered systems. In the non-ergodic diffusive regime, at energy $\epsilon>E_{c}$ ($E_{c}$ is the Thouless energy), it is shown to be completely determined by the weak…

The localization in a disordered system of $N$ interacting spins coupled by the long-range anisotropic interaction $1/R^{\alpha}$ is investigated using a finite size scaling in a $d=1$ -dimensional system for $N=8, 10, 12, 14$. The results…

The topological hypothesis claims that phase transitions in a classical statistical mechanical system are related to changes in the topology of the level sets of the Hamiltonian. So far, the study of this hypothesis has been restricted to…

We investigate the self-organization of point-particles with short-range interactions modeled via simple 1D and 2D Hubbard-like models. We show how various properties emerge such as, boson-like ordering leading to topological structures in…

Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has…

Minimal varying $\Lambda$ theories are defined by an action built from the Einstein-Cartan-Holst first order action for gravity with the cosmological constant $\Lambda$ as an independent scalar field, and supplemented by the Euler and…

Topological phases support edge states that can be robust to material deformations and other perturbations. While well-studied in quantum systems, topological phases have also been observed in stochastic and biochemical systems, yet it…

Inspired by the localization phenomenon in condensed matter systems, we explore constructions in the theory space of multiple scalar fields, in which exponentially suppressed couplings could originate from random parameters. In particular,…

When a low dimensional chaotic attractor is embedded in a three dimensional space its topological properties are embedding-dependent. We show that there are just three topological properties that depend on the embedding: parity, global…

We study ferromagnetic Ising models on finite graphs with an inhomogeneous external field, where a subset of vertices is designated as the boundary. We show that the influence of boundary conditions on any given spin is maximised when the…

We discuss the low energy theory of two-dimensional metals near the onset of spin density wave order. It is well known that such a metal has a superconducting instability induced by the formation of spin-singlet pairs of electrons, with the…

We address the problem of stability of one-dimensional non-periodic ground-state configurations with respect to finite-range perturbations of interactions in classical lattice-gas models. We show that a relevant property of non-periodic…

Few-body physics plays a central role in many branches of physics, such as nuclear physics and atomic physics. Advances in controlling ultra-cold quantum gases provide an ideal testbed for few-body physics theory. In this work, we study…

We study the compositeness of near-threshold quasi-bound states in the framework of effective field theory. From the viewpoint of the low-energy universality, we revisit the model-independent relations between the structure of the bound…

We study a two-dimensional system of spin-polarized fermions on the kagome lattice at filling fraction f=1/3 interacting through a nearest-neighbor interaction V. Above a critical interaction strength V_c a charge-density wave with a broken…