Connection probabilities and RSW-type bounds for the two-dimensional FK Ising model

CONNECTION BETWEEN THE KdV EQUATION AND THE TWO - DIMENSIONAL ISING MODEL

Among the various profound but solvable models tion [41 of physics, two of the most studied are the Korteweg— d2v 1 dv 2 1 dv 1 de Vries (KdV) equation for nonlinear wave phenom—i + —(av~+ i3) + ‘yu3 +-~(2) enon [1] and the two-dimensional Ising model [2] for statistical mechanics. It has been known [3] for severwherey is the independent variable and a, j3, y, and 6 al years that a Painlevé tra...

Folding probabilities: a novel approach to folding transitions and the two-dimensional Ising-model.

The theoretical concept of folding probability, p(fold), has proven to be a useful means to characterize the kinetics of protein folding. Here, we illustrate the practical importance of p(fold) and demonstrate how it can be determined theoretically. We derive a general analytical expression for p(fold) and show how it can be estimated from simulations for systems where the transition rates betw...

Ising Exponents in the Two-dimensional Site-diluted Ising Model

We study the site-diluted Ising model in two dimensions with Monte Carlo simulations. Using nite-size scaling techniques we compute the critical exponents observing deviations from the pure Ising ones. The diierences can be explained as the eeects of logarithmic corrections, without requiring to change the Universality Class.

Crossing probabilities on same-spin clusters in the two-dimensional Ising model

Probabilities of crossing on same-spin clusters, seen as order parameters, have been introduced recently for the critical 2d Ising model by Langlands, Lewis and SaintAubin. We extend Cardy’s ideas, introduced for percolation, to obtain an ordinary differential equation of order 6 for the horizontal crossing probability πh. Due to the identity πh(r)+πh(1/r) = 1, the function πh must lie in a 3-d...

Measures for Complexity and the Two-dimensional Ising model