Abstract
We show that a 2D system of free electrons on a square lattice with hoping between more than nearest neighbours is characterised by two quantum critical points associated with a change in topology of Fermi surface as a function of electron concentration. This simple model (when taking into account a positive interaction in a triplet channel) allows us to consistently explain some crucial experiments in the underdoped regime of hole-doped high- T c cuprates (ARPES, neutron scattering).
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