Glassy Dynamics in a Frustrated Spin System: Role of Defects

As Phil Anderson noted long ago, frustration can be generally defined by measuring the fluctuations in the coupling energy across a plane boundary between two large blocks of material. Since that time, a number of groups have studied the free energy fluctuations between (putative) distinct spin glass thermodynamic states. While upper bounds on such fluctuations have been obtained, useful lower bounds have been more difficult to derive. I present a history of these efforts, an...

In simulations of some infinite range spin glass systems with finite connectivity, it is found that for any resonable computational time, the saturatedenergy per spin that is achieved by a cluster algorithm is lowered in comparison to that achieved by Metropolis dynamics.The gap between the average energies obtained from these two dynamics is robust with respect to variations of the annealing schedule. For some probability distribution of the interactions the ground state ene...

A range of ferroic glasses, magnetic, polar, relaxor and strain glasses, are considered together from the perspective of spin glasses. Simple mathematical modelling is shown to provide a possible conceptual unification to back similarities of experimental observations, without considering all possible complexities and alternatives.

Spin glasses are disordered magnetic systems that exhibit a variety of properties that are characteristic of complex systems. After a brief review of basic spin glass concepts, their use in areas such as computer science, biology, and other fields will be explored. This use and its underlying basis will be termed old complexity. Newer concepts and ideas flowing from more recent studies of spin glasses will then be discussed, leading to a proposal for a kind of new complexity.

A spin glass is a diluted magnetic material in which the magnetic moments are randomly interacting, with a huge number of metastable states which prevent reaching equilibrium. Spin-glass models are conceptually simple, but require very sophisticated treatments. These models have become a paradigm for the understanding of glassy materials and also for the solution of complex optimization problems. After cooling from the paramagnetic phase, the spin glass remains out of equilib...

Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behaviour of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of...

Spin glasses are notoriously difficult to study both analytically and numerically due to the presence of frustration and metastability. Their highly non-convex landscapes require collective updates to explore efficiently. Currently, most state-of-the-art algorithms rely on stochastic spin clusters to perform non-local updates, but such "cluster algorithms" lack general efficiency. Here, we introduce a non-equilibrium approach for simulating spin glasses based on classical dyn...

We propose a new scenario for glassy dynamics in frustrated systems with no quenched-in randomness, based on jamming of extended dynamical structures near a critical point. This route to a glassy state is demonstrated in a lattice model of fluctuating lines. Numerical simulations of the model show non-exponential relaxations and diverging energy barriers in the vicinity of a thermodynamic phase transition. A master equation for the coarse grained dynamics is constructed. It s...

We give an overview of numerical and experimental estimates of critical exponents in Spin Glasses. We find that the evidence for a breakdown of universality of exponents in these systems is very strong.

We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a $d$-dimensional simple hypercubic lattice, in the limit of infinite dimensionality $d \to \infty$. In the analysis we consider a class of models in which the matrix of exchange constants is a linear combination of powers of the adjacency matrix. This choice leads to a special property: the Fourier transform of the exchange coupling $J(\ma...