Critical behavior of the Ising model with long range interactions

We present results of a Monte Carlo study for the ferromagnetic Ising model with long range interactions in two dimensions. This model has been simulated for a large range of interaction parameter $\sigma$ and for large sizes. We observe that the results close to the change of regime from intermediate to short range do not agree with the renormalization group predictions.Comment: 5 pages + 1 fi

A Study of Cross-Over Effects For The 2D Random Bond Potts Model

We present results of a numerical simulation of the $q$-state random bond Potts model in two dimensions and for large $q$. In particular, care is taken to study the crossover from the pure model to the random model, as well as the crossover from the percolation to the random model. We show how to determine precisely the random fixed point and measure critical exponents at this point.Comment: 12 pages, Latex, 2 eps figure

Numerical study of the Ising spin glass in a magnetic field

We study the order parameter distribution P(q) in the 4d Ising spin glass with $\pm J$ couplings in a magnetic field. We also compare these results with simulations for the infinite ranged model (i.e. SK model.) Then we analyse our numerical results in the framework of the droplet picture as well as in the mean field approach.Comment: 11 pages + 3 figures, LateX, figures uuencoded at the end of fil

On the phase transition of the 3D random field Ising model

We present numerical simulations of the random field Ising model in three dimensions at zero temperature. The critical exponents are found to agree with previous results. We study the magnetic susceptibility by applying a small magnetic field perturbation. We find that the critical amplitude ratio of the magnetic susceptibilities to be very large, equal to 233.1 \pm 1.5. We find strong sample to sample fluctuations which obey finite size scaling. The probability distribution of the size of small energy excitations is maximally non-self averaging, obeying a double peak distribution, and is finite size scaling invariant. We also study the approach to the thermodynamic limit of the ground state magnetization at the phase transition.Comment: Revised manuscript close to published versio

Frozen into stripes: fate of the critical Ising model after a quench

In this work we study numerically the final state of the two dimensional ferromagnetic critical Ising model after a quench to zero temperature. Beginning from equilibrium at $T_c$, the system can be blocked in a variety of infinitely long lived stripe states in addition to the ground state. Similar results have already been obtained for an infinite temperature initial condition and an interesting connection to exact percolation crossing probabilities has emerged. Here we complete this picture by providing a new example of stripe states precisely related to initial crossing probabilities for various boundary conditions. We thus show that this is not specific to percolation but rather that it depends on the properties of spanning clusters in the initial state.Comment: 4 pages, 5 figure

Diluted Antiferromagnetic 3D Ising model in a field

We present numerical simulations for the diluted antiferromagnetic 3D Ising model (DAFF) in an external magnetic field at zero temperature. Our results are compatible with the DAFF being in the same universality class as the Random Field Ising model, in agreement with the renormalization group prediction

A conformal bootstrap approach to critical percolation in two dimensions

We study four-point functions of critical percolation in two dimensions, and more generally of the Potts model. We propose an exact ansatz for the spectrum: an infinite, discrete and non-diagonal combination of representations of the Virasoro algebra. Based on this ansatz, we compute four-point functions using a numerical conformal bootstrap approach. The results agree with Monte-Carlo computations of connectivities of random clusters.Comment: 16 pages, Python code available at https://github.com/ribault/bootstrap-2d-Python, v2: some clarifications and minor improvement

Correlation functions for the 2D random bonds Potts Models

We study the spin-spin and energy-energy correlation functions for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach of the perturbation series around the conformal field theories representing the pure models. For the Ising model, we obtain a crossover in the amplitude for the correlation functions which doesn't change the critical exponent. For the $3$-state Potts model, we found a shift in the critical exponent produced by randomness. A comparison with numerical data is discussed briefly.Comment: To appear in the Proccedings of the Trieste Conference on Recent Developments in Statistical Mechanics and Quantum Field Theory, April 1995, 9 pages, latex, no figures, espcrc2.st

Order-parameter fluctuations (OPF) in spin glasses: Monte Carlo simulations and exact results for small sizes

The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in \cite{RS} which show that two of these parameters, $G$ and $G_c$, take universal values in the $\lim_{T\to 0}$. In this paper we present a detailed study of parameters measuring OPF for two mean-field models with and without time-reversal symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a field and the Ising p-spin glass (p=3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite volume. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the finite $T$ behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for $T_c$ and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters defined in terms of connected quantities are the proper ones to look at.Comment: 23 pages, REVTeX, 11 eps figure

A morphological study of cluster dynamics between critical points

We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising model and we use numerical methods to characterize the morphological and statistical properties of spin and Fortuin-Kasteleyn clusters during the critical evolution. The analysis of the dynamics of an out of equilibrium interface is also performed. We show that the small scale properties, smaller than the target critical growing length $\xi(t) \sim t^{1/z}$ with $z$ the dynamic exponent, are characterized by equilibrium at the working critical point, while the large scale properties, larger than the critical growing length, are those of the initial critical point. These features are similar to what was found for sub-critical quenches. We argue that quenches between critical points could be amenable to a more detailed analytical description.Comment: 26 pages, 13 figure