Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
1997-09-24
Phys. Rev. B 57 (1998) 11404
Physics
Condensed Matter
Disordered Systems and Neural Networks
18 pages RevTeX (multicolumn), eps-figures included
Scientific paper
10.1103/PhysRevB.57.11404
We study the critical and off-critical (Griffiths-McCoy) regions of the random transverse-field Ising spin chain by analytical and numerical methods and by phenomenological scaling considerations. Here we extend previous investigations to surface quantities and to the ferromagnetic phase. The surface magnetization of the model is shown to be related to the surviving probability of an adsorbing walk and several critical exponents are exactly calculated. Analyzing the structure of low energy excitations we present a phenomenological theory which explains both the scaling behavior at the critical point and the nature of Griffiths-McCoy singularities in the off-critical regions. In the numerical part of the work we used the free-fermion representation of the model and calculated the critical magnetization profiles, which are found to follow very accurately the conformal predictions for different boundary conditions. In the off-critical regions we demonstrated that the Griffiths-McCoy singularities are characterized by a single, varying exponent, the value of which is related through duality in the paramagnetic and ferromagnetic phases.
Igloi Ferenc
Rieger Heiko
No associations
LandOfFree
The Random Transverse Ising Spin Chain and Random Walks 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 The Random Transverse Ising Spin Chain and Random Walks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Random Transverse Ising Spin Chain and Random Walks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-318832