Strongly solid group factors which are not interpolated free group factors

We give examples of non-amenable ICC groups $\Gamma$ with the Haagerup property, weakly amenable with constant \Lambda_{\cb}(\Gamma) = 1, for which we show that the associated ${\rm II_1}$ factors $L(\Gamma)$ are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra $P \subset L(\Gamma)$ generates an amenable von Neumann algebra. Nevertheless, for these examples of groups $\Gamma$, $L(\Gamma)$ is not isomorphic to any interpolated free group factor L(\F_t), for $1 < t \leq \infty$.Comment: 20 page

A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses

A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional +/-J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 100^2 down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential and not as a power law as T -> Tc = 0.Comment: 6 pages, 9 figures, section 2 completly rewritte

The wormhole move: A new algorithm for polymer simulations

A new Monte Carlo move for polymer simulations is presented. The ``wormhole'' move is build out of reptation steps and allows a polymer to reptate through a hole in space; it is able to completely displace a polymer in time N^2 (with N the polymer length) even at high density. This move can be used in a similar way to configurational bias, in particular it allows grand canonical moves, it is applicable to copolymers and can be extended to branched polymers. The main advantage is speed since it is exponentially faster in N than configurational bias, but is also easier to program.Comment: 8 pages, 6 figure

Reply to Comment on "Ising Spin Glasses in a Magnetic Field"

The problem of the survival of a spin glass phase in the presence of a field has been a challenging one for a long time. To date, all attempts using equilibrium Monte Carlo methods have been unconclusive. In their comment to our paper, Marinari, Parisi and Zuliani use out-of-equilibrium measurements to test for an Almeida-Thouless line. In our view such a dynamic approach is not based on very solid foundations in finite dimensional systems and so cannot be as compelling as equilibrium approaches. Nevertheless, the results of those authors suggests that there is a critical field near B=0.4 at zero temperature. In view of this quite small value (compared to the mean field value), we have reanalyzed our data. We find that if finite size scaling is to distinguish between that small field and a zero field, we would need to go to lattice sizes of about 20x20x20.Comment: reply to comment cond-mat/9812401 on ref. cond-mat/981141