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C. M. Newman

Publications and source records attributed to C. M. Newman.

63 records · Page 4Linked to original sources
arXiv1999

Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t) of spins not flipped by time t decays to zero like t^[-theta(d)] for low d; for high d, p(t) may decay to p(infinity)>0, because of ``blocking'' (but perhaps still like a power). What are the effects of disorder or changes of lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples --- one disordered and one homogeneous --- where p(t) decays exponentially to p(infinity).

cond-mat.dis-nn↗
arXiv1998

Equilibrium Pure States and Nonequilibrium Chaos

We consider nonequilibrium systems such as the Edwards-Anderson Ising spin glass at a temperature where, in equilibrium, there are presumed to be (two or many) broken symmetry pure states. Following a deep quench, we argue that as time goes to infinity, although the system is usually in some pure state locally, either it never settles permanently on a fixed lengthscale into a single pure state, or it does but then the pure state depends on both the initial spin configuration and the realization of the stochastic dynamics. But this latter case can occur only if there exists an uncountable number of pure states (for each coupling realization) with almost every pair having zero overlap. In both cases, almost no initial spin configuration is in the basin of attraction of a single pure state; that is, the configuration space (resulting from a deep quench) is all boundary (except for a set of measure zero). We prove that the former case holds for deeply quenched two-dimensional ferromagnets. Our results raise the possibility that even if more than one pure state exists for an infinite system, time averages don't necessarily disagree with Boltzmann averages.

cond-mat.dis-nn↗
arXiv1997

Simplicity of State and Overlap Structure in Finite-Volume Realistic Spin Glasses

We present a combination of heuristic and rigorous arguments indicating that both the pure state structure and the overlap structure of realistic spin glasses should be relatively simple: in a large finite volume with coupling-independent boundary conditions, such as periodic, at most a pair of flip-related (or the appropriate number of symmetry-related in the non-Ising case) states appear, and the Parisi overlap distribution correspondingly exhibits at most a pair of delta-functions at plus/minus the self-overlap. This rules out the nonstandard SK picture introduced by us earlier, and when combined with our previous elimination of more standard versions of the mean field picture, argues against the possibility of even limited versions of mean field ordering in realistic spin glasses. If broken spin flip symmetry should occur, this leaves open two main possibilities for ordering in the spin glass phase: the droplet/scaling two-state picture, and the chaotic pairs many-state picture introduced by us earlier. We present scaling arguments which provide a possible physical basis for the latter picture, and discuss possible reasons behind numerical observations of more complicated overlap structures in finite volumes.

cond-mat.dis-nn↗
arXiv1996

The metastate approach to thermodynamic chaos

In realistic disordered systems, such as the Edwards-Anderson (EA) spin glass, no order parameter, such as the Parisi overlap distribution, can be both translation-invariant and non-self-averaging. The standard mean-field picture of the EA spin glass phase can therefore not be valid in any dimension and at any temperature. Further analysis shows that, in general, when systems have many competing (pure) thermodynamic states, a single state which is a mixture of many of them (as in the standard mean-field picture) contains insufficient information to reveal the full thermodynamic structure. We propose a different approach, in which an appropriate thermodynamic description of such a system is instead based on a metastate, which is an ensemble of (possibly mixed) thermodynamic states. This approach, modelled on chaotic dynamical systems, is needed when chaotic size dependence (of finite volume correlations) is present. Here replicas arise in a natural way, when a metastate is specified by its (meta)correlations. The metastate approach explains, connects, and unifies such concepts as replica symmetry breaking, chaotic size dependence and replica non-independence. Furthermore, it replaces the older idea of non-self-averaging as dependence on the bulk couplings with the concept of dependence on the state within the metastate at fixed coupling realization. We use these ideas to classify possible metastates for the EA model, and discuss two scenarios introduced by us earlier --- a nonstandard mean-field picture and a picture intermediate between that and the usual scaling/droplet picture.

cond-mat.dis-nn↗
arXiv1995

Spatial Inhomogeneity and Thermodynamic Chaos

We present a coherent approach to the competition between thermodynamic states in spatially inhomogeneous systems, such as the Edwards-Anderson spin glass with a fixed coupling realization. This approach explains and relates chaotic size dependence, ``dispersal of the metastate'', and for replicas: non-independence, symmetry breaking, and overlap (non-)self-averaging.

adap-org↗
arXiv1995

Non-Mean-Field Behavior of Realistic Spin Glasses

We provide rigorous proofs which show that the main features of the Parisi solution of the Sherrington-Kirkpatrick spin glass are not valid for more realistic spin glass models in any dimension and at any temperature.

adap-org↗
arXiv1995

Ground State Structure in a Highly Disordered Spin Glass Model

We propose a new Ising spin glass model on $Z^d$ of Edwards-Anderson type, but with highly disordered coupling magnitudes, in which a greedy algorithm for producing ground states is exact. We find that the procedure for determining (infinite volume) ground states for this model can be related to invasion percolation with the number of ground states identified as $2^{\cal N}$, where ${\cal N} = {\cal N}(d)$ is the number of distinct global components in the ``invasion forest''. We prove that ${\cal N}(d) = \infty$ if the invasion connectivity function is square summable. We argue that the critical dimension separating ${\cal N} = 1$ and ${\cal N} = \infty$ is $d_c = 8$. When ${\cal N}(d) = \infty$, we consider free or periodic boundary conditions on cubes of side length $L$ and show that frustration leads to chaotic $L$ dependence with {\it all} pairs of ground states occuring as subsequence limits. We briefly discuss applications of our results to random walk problems on rugged landscapes.

adap-org↗
arXiv1994

A New Look at Broken Ergodicity

We study the nature and mechanisms of broken ergodicity (BE) in specific random walk models corresponding to diffusion on random potential surfaces, in both one and high dimension. Using both rigorous results and nonrigorous methods, we confirm several aspects of the standard BE picture and show that others apply in one dimension, but need to be modified in higher dimensions. These latter aspects include the notions that at fixed temperature confining barriers increase logarithmically with time, that ``components'' are necessarily bounded regions of state space which depend on the observational timescale, and that the system continually revisits previously traversed regions of state space. We examine our results in the context of several experiments, and discuss some implications of our results for the dynamics of disordered and/or complex systems.

adap-org↗