The fully frustrated XY model revisited: a new universality class
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Universidade Federal de Minas Gerais
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The two-dimensional (2d) fully frustrated Planar Rotator model on a square lattice has been
the subject of a long controversy due to the simultaneous Z2 and O(2) symmetry existing in
the model. The O(2) symmetry being responsible for the Berezinskii–Kosterlitz–Thouless
transition (B K T ) while the Z2 drives an Ising-like transition. There are arguments supporting
two possible scenarios, one advocating that the loss of I sing and B K T order take place at
the same temperature Tt and the other that the Z2 transition occurs at a higher temperature
than the B K T one. In the first case an immediate consequence is that this model is in a new
universality class. Most of the studies take hand of some order parameter like the stiffness,
Binder’s cumulant or magnetization to obtain the transition temperature. Considering that the
transition temperatures are obtained, in general, as an average over the estimates taken about
several of those quantities, it is difficult to decide if they are describing the same or slightly
separate transitions. In this paper we describe an iterative method based on the knowledge of
the complex zeros of the energy probability distribution to study the critical behavior of the
system. The method is general with advantages over most conventional techniques since it
does not need to identify any order parameter a priori. The critical temperature and exponents
can be obtained with good precision. We apply the method to study the Fully Frustrated
Planar Rotator (F F P R) and the Anisotropic Heisenberg (F F X Y ) models in two dimensions.
We show that both models are in a new universality class with T P R = 0.45286(32) and
T X Y = 0.36916(16) respectively and the transition exponent ν = 0.824(30) ( 1
ν = 1.22(4)).
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Phase transitions
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https://link.springer.com/article/10.1007/s10955-019-02271-x