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

Using analytic and numerical methods, we study a $2d$ Hamiltonian model of interacting particles carrying ferro-magnetically coupled continuous spins which are also locally coupled to their own velocities. This model has been characterised…

Networks of particles connected by springs model many condensed-matter systems, from colloids interacting with a short-range potential, to complex fluids near jamming, to self-assembled lattices, to origami-inspired materials. Under small…

We study the effects of random bonds on spin chains that have an excitation gap in the absence of randomness. The dimerized spin-1/2 chain is our principal example. Using an asymptotically exact real space decimation renormalization group…

Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder these systems can…

We consider a quantum many-body model describing a system of electrons interacting with themselves and hopping from one ion to another of a one dimensional lattice. We show that the ground state energy of such system, as a functional of the…

This paper is second in the series, following Pranav et al. (2019), focused on the characterization of geometric and topological properties of 3D Gaussian random fields. We focus on the formalism of persistent homology, the mainstay of…

A dimensionless parameter $\Lambda$ is proposed to describe a hierarchy of morphologies in two-dimensional (2D) aggregates formed due to varying competition between short-range attraction and long-range repul- sion. Structural transitions…

We discuss with the aid of random walk arguments and exact numerical computations the magnetization properties of one-dimensional random field chains. The ground state structure is explained in terms of absorbing and non-absorbing random…

Weakly interacting Fermi gases exhibit rich collective dynamics in spin-dependent potentials, arising from correlations between spin degrees of freedom and conserved single atom energies, offering broad prospects for simulating many-body…

Complex systems often exhibit highly structured network topologies that reflect functional constraints. In this work, we investigate how, under varying combinations of system-wide selection rules and special agents, different classes of…

We demonstrate that in the system with anisotropic distribution of the defect-induced random local field directions in the n-dimensional space of vector order parameter with the O(n) symmetry, the defect-induced effective anisotropy arises…

Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…

Topological phases protected by symmetry can occur in gapped and---surprisingly---in critical systems. We consider non-interacting fermions in one dimension with spinless time-reversal symmetry. It is known that the phases are classified by…

Topological phases of matter are primarily studied in systems with short-range interactions. In nature, however, non-relativistic quantum systems often exhibit long-range interactions. Under what conditions topological phases survive such…

A simple geometrical characterization of configuration space neighborhoods of local energy minima in spin glass landscapes is found by exhaustive search. Combined with previous Monte Carlo investigations of thermal domain growth, it allows…

The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of self-organization because energy is a local property of a configuration. For…

We consider the weakly first order phase transition between the isotropic and ordered phases of nematics in terms of the behavior of topological line defects. Analytical and Monte Carlo results are presented for a new coarse-grained lattice…

The problem of finding the minimum-energy configuration of particles on a lattice, subject to a generic short-ranged repulsive interaction, is studied analytically. The study is relevant to charge ordered states of interacting fermions, as…

Carrying out perturbations around a lattice topological field theory in two dimensions, we show that it is on a first order phase transition fixed point with multiplicity ${n(n-1)/2}$, where $n$ is the number of its independent physical…

We investigate the spin structure of many-fermion systems with a spin-conserving two-body random interaction. We find a strong dominance of spin-0 ground states and considerable correlations between energies and wave functions of low-lying…