Related papers: The Hierarchical Parity Model
We discuss interfaces in spin glasses. We present new theoretical results and a numerical method to characterize overlap interfaces and the stability of the spin-glass phase in extended disordered systems. We use this definition to…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
We consider the long-ranged Ising spin-glass with random couplings decaying as a power-law of the distance, in the region of parameters where the spin-glass phase exists with a positive droplet exponent. For the Metropolis single-spin-flip…
We present an algorithm for the optimization and thermal equilibration of spin glasses - or more generally, cost functions of the Ising form $H=\sum_{\langle i j\rangle} J_{ij} s_i s_j + \sum_i h_i s_i$, defined on graphs with arbitrary…
The recursion relations of hierarchical models are studied and contrasted with functional renormalisation group equations in corresponding approximations. The formalisms are compared quantitatively for the Ising universality class, where…
We generate equilibrium configurations for the three and four dimensional Ising spin glass with Gaussian distributed couplings at temperatures well below the transition temperature T_c. These states are analyzed by a recently proposed…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
We introduce a hierarchical class of approximations of the random Ising spin glass in $d$ dimensions. The attention is focused on finite clusters of spins where the action of the rest of the system is properly taken into account. At the…
The one-dimensional long-range Ising spin glass provides useful insights into the properties of finite dimensional spin glasses with short-range interactions. The defect energy renormalization group equations derived for it by Kotliar,…
A renormalization group transformation suitable for spin glass models and, more generally, for disordered models, is presented. The procedure is non-standard in both the nature of the additional interactions and the coarse graining…
Spin glasses, generally defined as disordered systems with randomized competing interactions, are a widely investigated complex system. Theoretical models describing spin glasses are broadly used in other complex systems, such as those…
Here is the first part of the summary of my work on random Ising model using real-space renormalization group (RSRG), also known as a Migdal-Kadanoff one. This approximate renormalization scheme was applied to the analysis thermodynamic…
Recent numerical simulations indicate that several different equilibrium glass transitions may be characterized by diverging correlation lengths, and that these divergences are described by a non-mean-field, Ising-like, critical exponent. I…
Recent studies on the spin and the chirality orderings of the three-dimensional Heisenberg spin glass and related systems are reviewed with particular emphasis on the possible spin-chirality decoupling phenomena. Chirality scenario of real…
We consider the Dyson hierarchical version of the quantum Spin-Glass with random Gaussian couplings characterized by the power-law decaying variance $\overline{J^2(r)} \propto r^{-2\sigma}$ and a uniform transverse field $h$. The ground…
We study the phenomenon of the locking of the order parameter (or synchronization) in spin glasses at low temperatures. When two systems with independent disorders are coupled, their overlaps become similar. A crucial question is how this…
Financial markets are a classical example of complex systems as they comprise many interacting stocks. As such, we can obtain a surprisingly good description of their structure by making the rough simplification of binary daily returns.…
Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that…
Starting from preferences on N proposed policies obtained via questionnaires from a sample of the electorate, an Ising spin-glass model in a field can be constructed from which a political party could find the subset of the proposed…
Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that…