Hierarchical Low-Temperature Behaviour of One-Dimensional Incommensurate Structures

Abstract

The melting of a one-dimensional incommensurate structure in the nonanalytical regime is analysed. This study is done by a new technique of renormalization in real space with unequal blocks determined by the continued fraction expansion of the incommensurability ratio of the ground state. We have found that the variation of the specific heat at low temperatures consists of an infinite series of Schottky anomalies which corresponds to a hierarchical melting of the incommensurate chain. Our results modify and complete earlier studies which were developed for the interpretation of the anomalous low-temperature behaviour of the specific heat of hollandite.