Related papers: Fluctuations in Mean-Field Ising models
We consider ferromagnetic Ising models on graphs that converge locally to trees. Examples include random regular graphs with bounded degree and uniformly random graphs with bounded average degree. We prove that the "cavity" prediction for…
We have recently shown that in non-equilibrium spin systems at criticality the limit $\Xin$ of the fluctuation-dissipation ratio X(t,tw) for t >> tw >> 1 can be measured using observables such as magnetization or energy [Phys. Rev.\ E {\bf…
We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the $\lambda \phi^4$…
We consider the fluctuations of regular functions $f$ of a Wigner matrix $W$ viewed as an entire matrix $f(W)$. Going beyond the well studied tracial mode, $\mathrm{Tr}[f(W)]$, which is equivalent to the customary linear statistics of…
We consider the effects of the non-local Ising-like "core spin" correlations on the order-parameter fluctuation contribution to the resistivity and thermodynamics of metals showing Ising-like order at finite temperature. We employ the…
The scaling of fluctuations in the distribution of ground-state energies or costs with the system size N for Ising spin glasses is considered using an extensive set of simulations with the Extremal Optimization heuristic across a range of…
We show that a nominal temperature can be consistently and uniquely defined everywhere in the phase diagram of large classes of nonequilibrium kinetic Ising spin models. In addition, we confirm the recent proposal that, at critical points,…
The zero-temperature transverse Ising chain carrying an energy flux j_E is studied with the aim of determining the nonequilibrium distribution functions, P(M_z) and P(M_x), of its transverse and longitudinal magnetizations, respectively. An…
A detailed analysis of damping and noise due to a {\it sd}-interaction in a thin ferromagnetic film sandwiched between two large normal metal layers is carried out. The magnetization is shown to obey in general a non-local equation of…
We derive fluctuation relations for a many-body quantum system prepared in a Generalised Gibbs Ensemble subject to a general nonequilibrium protocol. By considering isolated integrable systems, we find generalisations to the Tasaki-Crooks…
In [17], the authors have defined an annealed Ising model on random graphs and proved limit theorems for the magnetization of this model on some random graphs including random 2-regular graphs. Then in [11], we generalized their results to…
Density-wave instabilities have been observed and studied in a multitude of materials. Most recently, in the context of unconventional superconductors like the iron-based superconductors, they have excited considerable interest. We analyze…
We have observed reproducible conductance fluctuations at low temperature in a small GaAs:Si wire driven across the Anderson transition by the application of a gate voltage. We analyse quantitatively the log-normal conductance statistics in…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
We study Derrida's generalized random energy model in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic limit for all admissible values of parameters.…
We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the…
Order-disorder phase transition of the ferromagnetic Ising model is investigated on a series of two-dimensional lattices that have negative Gaussian curvatures. Exceptional lattice sites of coordination number seven are distributed on the…
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the…
We consider the ferromagnetic Ising model on a sequence of graphs $G_n$ converging locally weakly to a rooted random tree. Generalizing [Montanari, Mossel, Sly '11], under an appropriate "continuity" property, we show that the Ising…
We present a generalization of the spin-fluctuation theory of magnetism which allows us to treat the full rotational invariance of the exchange interaction. The approach is formulated in terms of the local density approximation plus…