Extended surface disorder in the quantum Ising chain
arXiv:cond-mat/9903447 · doi:10.1088/0305-4470/32/21/304
Abstract
We consider random extended surface perturbations in the transverse field Ising model decaying as a power of the distance from the surface towards a pure bulk system. The decay may be linked either to the evolution of the couplings or to their probabilities. Using scaling arguments, we develop a relevance-irrelevance criterion for such perturbations. We study the probability distribution of the surface magnetization, its average and typical critical behaviour for marginal and relevant perturbations. According to analytical results, the surface magnetization follows a log-normal distribution and both the average and typical critical behaviours are characterized by power-law singularities with continuously varying exponents in the marginal case and essential singularities in the relevant case. For enhanced average local couplings, the transition becomes first order with a nonvanishing critical surface magnetization. This occurs above a positive threshold value of the perturbation amplitude in the marginal case.
15 pages, 10 figures, Plain TeX. J. Phys. A (accepted)
References in corpus (10)
- Discrete scale invariance and complex dimensions
- A Numerical Study of the Random Transverse-Field Ising Spin Chain
- Inhomogeneous Systems with Unusual Critical Behaviour
- The Random Transverse Ising Spin Chain and Random Walks
- Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain
- Anomalous diffusion in disordered media and random quantum spin chains
- Density Profiles in Random Quantum Spin Chains
- Boundary and Bulk Phase Transitions in the Two Dimensional Q > 4 State Potts Model
- Quantum Critical Dynamics of the Random Transverse Field Ising Spin Chain
- Griffiths-McCoy Singularities in the Random Transverse-Field Ising Spin Chain