Related papers: Metastable configurations on the Bethe lattice
The statistical properties of the local optima (metastable states) of the infinite range Ising spin glass with p-spin interactions in the presence of an external magnetic field h are investigated analytically. The average number of optima…
We study the equilibrium properties of an Ising frustrated lattice gas with a mean field replica approach. This model bridges usual {\em Spin Glasses} and a version of {\em Frustrated Percolation} model, and has proven relevant to describe…
We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from…
In the spirit of multi-scale modeling, we develop a theoretical framework for spin-lattice coupling that connects, on the one hand, to ab initio calculations of spin-lattice coupling parameters and, on the other hand, to the magneto-elastic…
This article is divided into two parts. In the first part, we study the hierarchical phenomenon of metastability in low-temperature lattice models in the most general setting. Given an abstract dynamical system governed by a Hamiltonian…
A theory for the complexity of the Bethe lattice spin-glass is developed applying to the cavity-method scheme of Mezard and Parisi the results recently obtained in the context of the Sherrington-Kirkpatrick model. The crucial ingredient is…
The classical transverse field Ising spin- glass model with short-range interactions is investigated beyond the mean- field approximation for a real d- dimensional lattice. We use an appropriate nontrivial modification of the Bethe- Peierls…
We study the problem of determining the Hamiltonian of a fully connected Ising Spin Glass of $N$ units from a set of measurements, whose sizes needs to be ${\cal O}(N^2)$ bits. The student-teacher scenario, used to study learning in…
In order to elucidate the relationship between rate-independent hysteresis and metastability in disordered systems driven by an external field, we study the Gaussian RFIM at T=0 on regular random graphs (Bethe lattice) of finite…
In the presented article we present an algorithm for the computation of ground state spin configurations for the 2d random bond Ising model on planar triangular lattice graphs. Therefore, it is explained how the respective ground state…
We consider two systems of Ising spins with plaquette interactions. They are simple models of glasses which have dual representations as kinetically constrained systems. These models allow an explicit analysis using the mosaic, or entropic…
Replica field theory is used to study the n-dependent free energy of the Ising spin glass in a first order perturbative treatment. Large sample-to-sample deviations of the free energy from its quenched average prove to be Gaussian,…
We explore the breaking of rotational symmetry on the lattice for bound state energies and practical methods for suppressing this breaking. We demonstrate the general problems associated with lattice discretization errors and finite-volume…
In this note we study metastability phenomena for a class of long-range Ising models in one-dimension. We prove that, under suitable general conditions, the configuration -1 is the only metastable state and we estimate the mean exit time.…
The metastable states of a glass are counted by adding a weak pinning field which explicitly breaks the ergodicity. Their entropy, that is the logarithm of their number, is extensive in a range of temperatures $T_G < T < T_C$ only, where…
Two kinds of recursive lattices with the same coordination number but different unit cells (2-D square and 3-D cube) are constructed and the antiferromagnetic Ising model is solved exactly on them to study the stable and metastable states.…
We study numerically the number of single-spin-flip stable states in the T=0 Random Field Ising Model (RFIM) on random regular graphs of connectivity $z=2$ and $z=4$ and on the cubic lattice. The annealed and quenched complexities (i.e. the…
We study the metastable dynamics of a discretised version of the mass-conserving stochastic Allen-Cahn equation. Consider a periodic one-dimensional lattice with $N$ sites, and attach to each site a real-valued variable, which can be…
The non-equilibrium dynamics of a one-dimensional Ising model with uniform, short-ranged three-spin interactions is investigated. It is shown that this model possesses an exponentially large number of metastable configurations that are…
We study the L\'evy spin-glass model with the replica and the cavity method. In this model each spin interacts through a finite number of strong bonds and an infinite number of weak bonds. This hybrid behaviour of L\'evy spin glasses…