Absence of jump discontinuity in the magnetization in quasi-one-dimensional random-field Ising models

We consider the zero-temperature random-field Ising model in the presence of an external field, on ladders and in one dimension with finite range interactions, for unbounded continuous distributions of random fields, and show that there is no jump discontinuity in the magnetizations for any quasi-one-dimensional model. We show that the evolution of the system at an external field can be described by a stochastic matrix and the magnetization can be obtained using the eigenvector of the matrix corresponding to the eigenvalue one, which is continuous and differentiable function of the external field.

Figure 1

Two-leg ladder.

Figure 2

Magnetization curves for a two-ladder in the increasing field. $N=2^{23}$.

Figure 3

(a) Linear chain showing nearest and next neighbor interactions and (b) graph on which nearest neighbor interaction is equivalent to the linear chain with nearest and next neighbor interactions.

Figure 4

Magnetization curve in the increasing field for linear chain with nearest and next neighbor interactions. $N=2^{23}$.