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.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.

arXiv:cond-mat/9903447Journal of Physics A Mathematical and GeneralJan 1, 19997 citations

The magnetic transition in finite systems

W. F. Hall, Roger E. De Wames, T. Wolfram

Physics Letters AMay 1, 19711 citation

Low- and high-field induced uniform and staggered magnetizations of a spin ladder with DM term

P. N. Bibikov

Analytic expressions for uniform and staggered magnetizations of a spin ladder with a staggered Dzyaloshinskii-Moriya interaction along rungs are obtained in the lowest perturbative orders. The obtained formulas describe magnetic behavior in two marginal regions related to low ( $h\ll h_c$ ) and high ( $h\gg h_s$ ) magnetic fields.Analytic expressions for uniform and staggered magnetizations of a spin ladder with a staggered Dzyaloshinskii-Moriya interaction along rungs are obtained in the lowest perturbative orders. The obtained formulas describe magnetic behavior in two marginal regions related to low ($h\ll h_c$) and high ($h\gg h_s$) magnetic fields.

arXiv:0712.1349Dec 9, 20070 citations

Effective field methods with correlations in magnetic systems

Raf Dekeyser, G. Kamieniarz

Journal of Magnetism and Magnetic MaterialsFeb 1, 19923 citations

Magnetic Phases and Long-Range Ordering of the Haldane System in High Magnetic Fields

Isao Harada, Yoshihiro Nishiyama

Critical properties of field-induced magnetic phases are investigated in the one-dimensional S=1 Haldane system with planar anisotropy, using the finite-temperature density-matrix renormalization group method. We point out that the underlying physics of the properties differs significantly between cases of different field directions: The magnetic phase is characterized as the gapless Tomonaga-Luttinger regime in one case and as the gapful soliton regime in the other. In connection with the information obtained for the one-dimensional spin chain, possible implications for the field-induced magnetic long-range ordering are discussed.Critical properties of field-induced magnetic phases are investigated in the one-dimensional S=1 Haldane system with planar anisotropy, using the finite-temperature density-matrix renormalization group method. We point out that the underlying physics of the properties differs significantly between cases of different field directions: The magnetic phase is characterized as the gapless Tomonaga-Luttinger regime in one case and as the gapful soliton regime in the other. In connection with the information obtained for the one-dimensional spin chain, possible implications for the field-induced magnetic long-range ordering are discussed.

Progress of Theoretical Physics SupplementJan 1, 20022 citations

h\ll h_c

) and high (

h\gg h_s

) magnetic fields.