Random infinite-volume Gibbs states for the Curie-Weiss random field Ising model

Spin-Flip Dynamics of the Curie-Weiss Model: Loss of Gibbsianness with Possibly Broken Symmetry

“…In order to understand the symmetry breaking in the set of points of discontinuity in detail, we discuss the extended phase diagram of the quenched model, generalizing the known phase diagram from the symmetric case α = 0 [1,21,3] to non-symmetric distributions. It also has some interest in itself, beyond the study of non-Gibbsianness.…”

“…For the actual computations it is convenient to make a change of variables E = βε, M = βm and write We encounter two mechanisms of creation of new minima, a fold bifurcation and a pitchfork bifurcation [13,20]. This analysis has partially been done for the case α = 0 [21,1,3] and our analysis incorporates these results. There are moreover interesting new phenomena arising when we look at general, possibly non-zero α's.…”

Poincaré and logarithmic Sobolev constants for metastable Markov chains via capacitary inequalities

“…Suppose that the assumptions of Theorem 1.24 hold with ̺ = e −c 1 β N . Then, P h -a.s., for any c 2 ∈ (0, min{c 1 Finally, notice that sharp asymptotics of the mean hitting time including the precise prefactor has been establish in [8], which by the above identification gives an asymptotic sharp formula for the Poincaré constant of the random field Curie Weiss model.…”

Spherical Model in a Random Field

“…(34) the magnetization of the spherical model obtains the values ±m * with probability 1 2 , where m * is the spontaneous magnetization. The magnetization of the Curie-Weiss model and, most likely, of disordered finite-dimensional Ising models has the same distribution, see [3]. One can also guess that the magnetization of various disordered O(n) models is uniformly distributed over an n-dimensional sphere.…”