M. A. Moore

Lower critical dimension of Ising spin glasses: a numerical study

A transfer matrix method is used to study the variation with length scale L of the distribution PL(Jeff) of effective couplings in Ising spin glasses at zero temperature. For a gaussian initial distribution the authors find in two dimensions J(L) identical to ( mod Jeff mod ) varies as L-1 nu / for 2<or=L<or=12, with nu =3.4+or-0.1, implying a zero-temperature phase transition with correlation length exponent nu . In three dimensions the effective couplings initially increase with length scale, J(L) varies as L-1 nu / for 2<or=L<or=4, with -1/ nu approximately=0.2, suggesting a phase transition at finite temperature. The results are described surprisingly well by the zero-temperature version of the Migdal-Kadanoff renormalisation group scheme.

Theory of the polymer coil-globule transition

The change of a polymer from an extended coil form above the theta point to a dense globular form below the theta point is investigated in a self-consistent field approximation and found to be a second-order phase transition in the limit of an infinitely long polymer. Other theories of the transition are reviewed and further information obtained as to the dimensionality dependence of the transition by means of the analogy between the theta point and a tricritical point.

Evidence for the Droplet Picture of Spin Glasses

We have studied the Parisi overlap distribution for the three dimensional Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the full Parisi replica symmetry breaking, just as was also observed in recent Monte Carlo simulations on a cubic lattice. However, for lower temperatures our data agree with predictions from the droplet or scaling picture. The failure to see droplet model behaviour in Monte Carlo simulations is due to the fact that all existing simulations have been done at temperatures too close to the transition temperature so that sytem sizes larger than the correlation length have not been achieved.

Conformal invariance and stochastic Loewner evolution processes in two-dimensional Ising spin glasses.

We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can be related to that in a second geometry by a conformal transformation. We also present direct evidence that the domain walls are stochastic Loewner (SLE) processes with

Stiffness exponent of two-dimensional Ising spin glasses for nonperiodic boundary conditions using aspect-ratio scaling

\kappa \approx 2.1

Interface energies in ising spin glasses.

. An argument is given that their fractal dimension

Finite-size corrections in the Sherrington-Kirkpatrick model

d_f

Free energy fluctuations in Ising spin glasses

is related to their interface energy exponent

Corrections to scaling are large for droplets in two-dimensional spin glasses.

\theta

The link overlap and finite size effects for the 3D Ising spin glass

by