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Competing interactions on different length scales are responsible for the spontaneous formation of modulated phases -- patterns -- in many physical and chemical systems. In this thesis we investigate the magnetic domain patterns of atomically-thin iron films on the copper (001)-surface in the two-parameter space spanned by temperature and the applied magnetic field. Upon heating the sample in a constant applied field, we observe a transition from the uniform, saturated state to circular domains in a homogeneous background, the bubble state. This transition breaks the translational symmetry of the domain pattern and a second transition, leading from bubbles to regular stripes of alternating magnetization, breaks also the rotational symmetry: The phase diagram of the system shows systematic inverse symmetry breaking. In our experiments we observe scaling and universality also in this regime of inverse symmetry breaking. By exploiting these scaling properties, we can predict the phase diagram at high temperature from ground-state calculations and we find that the occurrence of inverse symmetry breaking is a consequence of the truly two-dimensional nature of our system. Dynamic aspects of the pattern formation are addressed in time-dependent measurements. We find that the temperature dependence of the relaxation times, measured in response to changing temperature or magnetic field, points towards a non-Arrhenius-like behaviour, as is typical in glassy systems.
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