Modulated phase of an ising system with competing interactions on a Cayley tree

Abstract

A system with competing nearest-neighbour and next-nearest-neighbour interactions is considered on a Cayley tree. The phase diagram contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature. The variation of the wavevector with temperature in the modulated phase is studied in detail, it shows narrow commensurate steps between incommensurate regions (“incomplete devil's staircase”). The behaviour of the coherence length near the different transitions is also analyzed.