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• W2065479908 startingPage "648" @default.
• W2065479908 abstract "We study a one-dimensional quantum Ising model where the exchange couplings and the transverse fields are hierarchically distributed. Exact analytical results for the critical line, energy gap, and dispersion relation of the low-energy excitations are obtained. It is shown that only in the case of ${mathit{R}}_{1}$=${mathit{R}}_{2}$=R>${mathit{R}}_{mathit{c}}$, where ${mathit{R}}_{1}$ and ${mathit{R}}_{2}$ are the hierarchical parameters for the exchange couplings and the transverse fields, does the system preserve the logarithmic singularity in the specific heat. Using renormalization-group techniques and an iteration map for the transfer matrix, we have presented the analytical results for the scaling properties for the energy spectra of the models with ${mathit{R}}_{1}$=${mathit{R}}_{2}$ and ${mathit{R}}_{2}$=1. From knowledge of the scaling properties of the energy spectra, we have exhibited a close relationship between the disappearance of the logarithmic singularity in the specific heat and the anomalous scaling behavior at the lower band edges." @default.
• W2065479908 created "2016-06-24" @default.
• W2065479908 creator A5049279485 @default.
• W2065479908 creator A5075057638 @default.
• W2065479908 date "1990-07-01" @default.
• W2065479908 modified "2023-10-18" @default.
• W2065479908 title "Phase transition and scaling properties of the energy spectrum for a hierarchical quantum Ising model" @default.
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• W2065479908 doi "https://doi.org/10.1103/physrevb.42.648" @default.
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