Related papers: Fractal geometry of spin-glass models
The fractal dimension of excitations in glassy systems gives information on the critical dimension at which the droplet picture of spin glasses changes to a description based on replica symmetry breaking where the interfaces are space…
Results are presented for the geometry of low-energy excitations in the one-dimensional Ising spin chain with power-law interactions, in which the model parameters are chosen to yield a finite spin-glass transition temperature. Both…
The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient…
The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction $w$ of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an…
Much of the information about the multi-valley structure of disordered spin systems can be convened in a simple tree structure -- a barrier tree -- the leaves and internal nodes of which represent, respectively, the local minima and the…
We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can…
The fractal dimension of domain walls produced by changing the boundary conditions from periodic to anti-periodic in one spatial direction is studied using both the strong-disorder renormalization group and the greedy algorithm for the…
Glasses are amorphous solids whose constituent particles are caged by their neighbors and thus cannot flow. This sluggishness is often ascribed to the free energy landscape containing multiple minima (basins) separated by high barriers.…
A controversial issue in spin glass theory is whether mean field correctly describes 3-dimensional spin glasses. If it does, how can replica symmetry breaking arise in terms of spin clusters in Euclidean space? Here we argue that there…
The local minima (inherent structures) of a system and their associated transition links give rise to a network. Here we consider the topological and distance properties of such a network in the context of spin glasses. We use steepest…
We discussed hierarchies and rescaling rule of the self similar transformations in Ising models, and define a fractal dimension of an ordered cluster, which minimum corresponds to a fixed point of the transformations. By the fractal…
The fractal structure of spin clusters and their boundaries in the critical two-dimensional (2D) Ising model is investigated numerically. The fractal dimensions of these geometrical objects are estimated by means of Monte Carlo simulations…
The p-spin spin-glass model has been studied extensively at mean-field level because of the insights which it provides into the mode-coupling approach to structural glasses and the nature of the glass transition. We demonstrate explicitly…
Nearest-neighbor-interaction Ising spin glasses are studied on three different hierarchical lattices, all of them belonging to the Wheatstone-Bridge family. It is shown that the spin-glass lower critical dimension in these lattices should…
We have studied the topology of the energy landscape of a spin-glass model and the effect of frustration on it by looking at the connectivity and disconnectivity graphs of the inherent structure. The connectivity network shows the adjacency…
Fractal geometries, characterized by self-similar patterns and non-integer dimensions, provide an intriguing platform for exploring topological phases of matter. In this work, we introduce a theoretical framework that leverages isospectral…
We study a two-dimensional compressible Ising spin glass at constant volume. The spin interactions are coupled to the distance between neighboring particles in the Edwards-Anderson model with +/- J interactions. We find that the energy of a…
We consider the effect of perturbing a single bond on ground-states of nearest-neighbor Ising spin-glasses, with a Gaussian distribution of the coupling constants, across various two and three-dimensional lattices and regular random graphs.…
We analyse the relationship between dynamics and configuration space structure of Ising spin glass systems. The exact knowledge of the structure of the low--energy landscape is used to study the relaxation of the system by random walk in…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…