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 (ξ ∼ e 2βJ ) and not as a power law as T → Tc = 0.PACS. 75.10.Nr Spin glass and other random models -02.70.Lq Monte Carlo and statistical methods

We perform Monte Carlo simulations of large two-dimensional Gaussian Ising spin glasses down to very low temperatures β = 1/T = 50. Equilibration is ensured by using a cluster algorithm including Monte Carlo moves consisting of flipping fundamental excitations. We study the thermodynamic behavior using the Binder cumulant, the spin-glass susceptibility, the distribution of overlaps, the overlap with the ground state and the specific heat. We confirm that Tc = 0. All results are compatible with an algebraic divergence of the correlation length with an exponent ν. We find −1/ν = −0.295(30), which is compatible with the value for the domain-wall and droplet exponent θ ≈ −0.29 found previously in ground-state studies. Hence the thermodynamic behavior of this model seems to be governed by one single exponent.

We present basic properties of dipolar stochastic Loewner evolutions, a new version of stochastic Loewner evolutions (SLEs) in which the critical interfaces end randomly on an interval of the boundary of a planar domain. We present a general argument explaining why correlation functions of models of statistical mechanics are expected to be martingales and we give a relation between dipolar SLEs and conformal field theories (CFTs). We compute SLE excursion and/or visiting probabilities, including the probability for a point to be on the left/right of the SLE trace or that for being inside the SLE hull. These functions, which turn out to be harmonic, have a simple CFT interpretation. We also present numerical simulations of the ferromagnetic Ising interface that confirm both the probabilistic approach and the CFT mapping.

We investigate the phase behavior of random copolymer melts via large-scale Monte Carlo simulations. The AB multiblock copolymers have, on average, symmetric composition and are characterized by a correlation λ along the polymer. We employ parallel tempering and the wormhole algorithm and a technique to reduce the variance between different realizations of the disorder to explore the phase behavior. For a very large correlation of blocks, we observe a sequence of disordered phase, macrophase separation and remixing into a spatially structured (lamellar or microemulsion-like) phase upon increasing the incompatibility between different monomer species as predicted by mean field theory. For smaller values of λ, we find that a locally segregated structure gradually forms as the incompatibility increases. As we increase the number of blocks in the polymers, the region of macrophase separation shrinks. The results of our Monte Carlo simulation are in agreement with a Ginzburg criterion, which suggests that mean field theory becomes worse as the number of blocks in a polymer increases. Different scenarios for the remixing at large incompatibility χ have been investigated. The simulation data exhibit large finite size effects. Depending on the parameters, the remixing might be either an unbinding transition, where the characteristic length scale of the spatially structured phase diverges, or a three-phase coexistence over an extended range of incompatibilities. In the latter case, the sequence distribution in the coexisting phases differs (fractionation).