Convolution of multifractals and the local magnetization in a random field Ising chain

Details Convolution of multifractals and the local magnetization in a random field Ising chain Convolution of multifractals and the local magnetization in a random field Ising chain

2001-02-19

arxiv.org/abs/cond-mat/0102328v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

An error in figure 1 was corrected, small additions were made to the introduction and the conclusions, some typos were correct

Scientific paper

10.1088/0305-4470/34/39/308

The local magnetization in the one-dimensional random-field Ising model is essentially the sum of two effective fields with multifractal probability measure. The probability measure of the local magnetization is thus the convolution of two multifractals. In this paper we prove relations between the multifractal properties of two measures and the multifractal properties of their convolution. The pointwise dimension at the boundary of the support of the convolution is the sum of the pointwise dimensions at the boundary of the support of the convoluted measures and the generalized box dimensions of the convolution are bounded from above by the sum of the generalized box dimensions of the convoluted measures. The generalized box dimensions of the convolution of Cantor sets with weights can be calculated analytically for certain parameter ranges and illustrate effects we also encounter in the case of the measure of the local magnetization. Returning to the study of this measure we apply the general inequalities and present numerical approximations of the D_q-spectrum. For the first time we are able to obtain results on multifractal properties of a physical quantity in the one-dimensional random-field Ising model which in principle could be measured experimentally. The numerically generated probability densities for the local magnetization show impressively the gradual transition from a monomodal to a bimodal distribution for growing random field strength h.

Affiliated with

Also associated with

No associations

Rating

Convolution of multifractals and the local magnetization in a random field Ising chain does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Convolution of multifractals and the local magnetization in a random field Ising chain, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convolution of multifractals and the local magnetization in a random field Ising chain will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-212297