  In this paper we present a study of pattern formation in bidimensional
systems with competing short-range attractive and long-range repulsive
interactions. The interaction parameters are chosen in such a way to analyse
two different situations: the spontaneous pattern formation due to the presence
of strong competing interactions on different length scales and the pattern
formation as a response to an external modulating potential when the system is
close to its Lifshitz point. We compare different Monte Carlo techniques
showing that Parallel Tempering technique represents a promising approach to
study such systems and we present detailed results for the specific heat and
the structural properties. We also present random phase approximation
predictions about the spontaneous pattern formation (or microphase separation),
as well as linear response theory predictions about the induced pattern
formation due to the presence of an external modulating field. In particular we
observe that the response of our systems to external fields is much stronger
compared to the response of a Lennard-Jones fluid.
