We present a renormalization argument for the discrete linear chain with a harmonic interparticle interaction and a sinusoidal substrate potential. We find that there exists a critical value of the substrate potential above which the incommensurate phase lying in between two successive registered phases is a complete devil's staircase of commensurate states. For weaker substrate potentials, the devil's staircase is partially incomplete. Near the commensurate-incommensurate transition it consists only of commensurate states, while at higher soliton densities the commensurate states are separated by truly incommensurate states. These results are in agreement with the findings of previous authors using different methods.We present a renormalization argument for the discrete linear chain with a harmonic interparticle interaction and a sinusoidal substrate potential. We find that there exists a critical value of the substrate potential above which the incommensurate phase lying in between two successive registered phases is a complete devil's staircase of commensurate states. For weaker substrate potentials, the devil's staircase is partially incomplete. Near the commensurate-incommensurate transition it consists only of commensurate states, while at higher soliton densities the commensurate states are separated by truly incommensurate states. These results are in agreement with the findings of previous authors using different methods.

Physical review. B, Condensed matterJan 1, 198312 citations

Commensurate-incommensurate transitions and the Lifshitz point in the quantum asymmetric clock model

Steven F. Howes

The asymmetric three-state clock model is studied in the context of a one-dimensional quantum Hamiltonian. Series expansions are used to investigate the commensurate-incommensurate transition and the incommensurate-liquid Kosterlitz-Thouless transition. Evidence is presented for a Lifshitz point at which the critical indices $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\gamma}$ are Potts-type, while the mass-gap index appears to take its Ising value, $\ensuremath{\nu}=1$.The asymmetric three-state clock model is studied in the context of a one-dimensional quantum Hamiltonian. Series expansions are used to investigate the commensurate-incommensurate transition and the incommensurate-liquid Kosterlitz-Thouless transition. Evidence is presented for a Lifshitz point at which the critical indices $\ensuremath{\alpha}$, $\ensuremath{\beta}$, and $\ensuremath{\gamma}$ are Potts-type, while the mass-gap index appears to take its Ising value, $\ensuremath{\nu}=1$.

Physical review. B, Condensed matterFeb 1, 198355 citations

Renormalization-group approach to commensurate-incommensurate transitions in two dimensions

M. W. Puga, Eugen Šimánek, H. Beck

We present a renormalization-group-approach analysis of the commensurate-incommensurate transition of the two-dimensional classical sine-Gordon system which includes incommensurability as a new renormalizable parameter. The critical behavior of various quantities shows corrections with respect to the simpler self-consistent harmonic approximation (SCHA). However, our result for the phase boundary still has a SCHA-type $T$ dependence, suggesting that incommensurability tends to suppress the role of fluctuations.We present a renormalization-group-approach analysis of the commensurate-incommensurate transition of the two-dimensional classical sine-Gordon system which includes incommensurability as a new renormalizable parameter. The critical behavior of various quantities shows corrections with respect to the simpler self-consistent harmonic approximation (SCHA). However, our result for the phase boundary still has a SCHA-type $T$ dependence, suggesting that incommensurability tends to suppress the role of fluctuations.

Physical review. B, Condensed matterSep 1, 198211 citations

T

dependence, suggesting that incommensurability tends to suppress the role of fluctuations.