Related papers: Ising Model of the Glassy Correlation Length
The excitation-chain theory of the glass transition, proposed in an earlier publication, predicts diverging, super-Arrhenius relaxation times and, {\it via} a similarly diverging length scale, suggests a way of understanding the relations…
Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been…
The four-dimensional +-J random-bond Ising model is studied using ground-state calculations. System sizes up to N=6^4 spins are considered. Here it is found that the ferromagnetic-spin glass transition occurs at a critical concentration…
The model of p Ising spins coupled to 2d gravity, in the form of a sum over planar phi-cubed graphs, is studied and in particular the two-point and spin-spin correlation functions are considered. We first solve a toy model in which only a…
We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We…
The unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granulars, spin glasses, superconductors, ...) is a sluggish dynamics at low temperatures. Indeed, their dynamics is so slow that thermal equilibrium is…
Enormous enhancement in the viscosity of a liquid near its glass transition is generally connected to the growing many-body static correlations near the transition, often coined as `amorphous ordering'. Estimating the length scales of such…
We have studied numerically the states reached in a quench from various temperatures in the one-dimensional fully-connected Kotliar, Anderson and Stein Ising spin glass model. This is a model where there are long-range interactions between…
Hierarchical spin-glasses are Ising spin models defined by recursively coupling together two equally-sized sub-systems. In this work a new hierarchical spin system is introduced wherein the sub-systems are recursively coupled together…
Glass-forming liquids display strong fluctuations -- dynamical heterogeneities -- near their glass transition. By numerically simulating a binary Weeks-Chandler-Andersen liquid and varying both temperature and timescale, we investigate the…
We study an effective spin model derived perturbatively from random transverse-field Ising model on the pyrochlore lattice. The model consists of spin-configurations on the pyrochlore lattice, restricted to the spin-ice subspace, with spins…
We study the 2-dimensional Ising model at critical temperature on a simply connected subset $\Omega_{\delta}$ of the square grid $\delta\mathbb{Z}^{2}$. The scaling limit of the critical Ising model is conjectured to be described by…
A detailed numerical study is made of relaxation at equilibrium in the Sherrington-Kirkpatrick Ising spin glass model, at and above the critical temperature Tg. The data show a long time stretched exponential relaxation q(t) ~…
Typical features of glass phenomenology such as the Vogel-Fulcher law, the Kauzmann paradox and the Adam-Gibbs relationship are shown to follow from the recently discovered mapping of glasses to Ising spin glasses in a magnetic field. There…
We study the glass formation in two- and three-dimensional Ising and Heisenberg spin systems subject to competing interactions and uniaxial anisotropy with a mean-field approach. In three dimensions, for sufficiently strong anisotropy the…
We propose that there exists a generic class of glass forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems…
The $q$-neighbor Ising model is investigated on homogeneous random graphs with a fraction of edges associated randomly with antiferromagnetic exchange integrals and the remaining edges with ferromagnetic ones. It is a nonequilibrium model…
Extensive equilibrium Monte Carlo simulations are performed for a three-dimensional Heisenberg spin glass with the nearest-neighbor Gaussian coupling to investigate its spin-glass and chiral-glass orderings. The occurrence of a…
We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for…
We revisited, by means of numerical simulations, the one dimensional bond diluted Levy Ising spin glasses outside the limit of validity of mean field theories. In these models the probability that two spins at distance $r$ interact (via a…