Transverse-field Ising spin chain with inhomogeneous disorder

Abstract

We consider the critical and off-critical properties at the boundary of the random transverse-field Ising spin chain when the distribution of the couplings and/or transverse fields, at a distance $l$ from the surface, deviates from its uniform bulk value by terms of order $l^{-\kappa }$ with an amplitude $A$. Exact results are obtained using a correspondence between the surface magnetization of the model and the surviving probability of a random walk with time-dependent absorbing boundary conditions. For slow enough decay, $\kappa <1/2$, the inhomogeneity is relevant: Either the surface stays ordered at the bulk critical point or the average surface magnetization displays an essential singularity, depending on the sign of $A$. In the marginal situation, $\kappa =1/2$, the average surface magnetization decays as a power law with a continuously varying, $A$-dependent, critical exponent which is obtained analytically. The behavior of the critical and off-critical autocorrelation functions as well as the scaling form of the probability distributions for the surface magnetization and the first gaps are determined through a phenomenological scaling theory. In the Griffiths phase, the properties of the Griffiths-McCoy singularities are not affected by the inhomogeneity. The various results are checked using numerical methods based on a mapping to free fermions.

11 pages (Revtex), 11 figures

References in corpus (8)

• The Random Transverse Ising Spin Chain and Random Walks
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• Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain
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Cited by in corpus (3)

• Strong disorder RG approach of random systems
• Multiscaling in Ising quantum chains with random Hilhorst-van Leeuwen perturbations
• Anomalous diffusion in a space- and time-dependent energy landscape