Phase transitions in monolayers adsorbed on uniaxial substrates

The phase diagram of a $p\times 1$ uniaxial adsorbed layer is investigated theoretically, including the possibility of incommensurate phases. For $p=3\mathrm{} \mathrm{and} 4$ we determine the incommensurability crossover exponents at the commensurate-fluid multicritical point. We then argue that due to a strong renormalization of the dislocation core energy the incommensurate phase should be stable up to the multicritical point for $p>~3$. Possible phase diagrams for general $p$ are discussed.