Roughening transitions of driven surface growth

Reverse monte carlo method and its implications for generalized cluster algorithms

We describe a novel switching algorithm based on a "reverse" Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of cluster-type Monte Carlo methods, and the generalization makes it possible to derive cluster algorithms for systems with both discrete and continuous degrees of freedom. The roughening transition in the sine-Gordon model has been studied with this method, and high-accuracy simulations for system sizes up to 1024(2) were carried out to examine the logarithmic divergence of the surface roughness above the transition temperature, revealing clear evidence for universal scaling of the Kosterlitz-Thouless type.

Apparent phase transitions in finite one-dimensional sine-Gordon lattices

We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model cannot have any phase transition [J. A. Cuesta and A. Sánchez, J. Phys. A 35, 2373 (2002)], Langevin as well as Monte Carlo simulations strongly suggest the existence of a finite temperature separating a flat from a rough phase. We explain this result by means of the transfer operator formalism and show as a consequence that sine-Gordon lattices of any practically achievable size will exhibit this apparent phase transition at unexpectedly large temperatures.