Energy probability distribution zeros : a route to study phase transitions.
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2017
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In the study of phase transitions a very few models are accessible to exact solution. In most cases analytical
simplifications have to be done or some numerical techniques have to be used to get insight about
their critical properties. Numerically, the most common approaches are those based on Monte Carlo
simulations together with finite size scaling analysis. The use of Monte Carlo techniques requires the
estimation of quantities like the specific heat or susceptibilities in a wide range of temperatures or the
construction of the density of states in large intervals of energy. Although many of these techniques
are well developed they may be very time consuming when the system size becomes large enough.
It should be suitable to have a method that could surpass those difficulties. In this work we present
an iterative method to study the critical behavior of a system based on the partial knowledge of the
complex Fisher zeros set of the partition function. 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 great precision even in the most unamenable cases
like the two dimensional XY model. To test the method and to show how it works we applied it to
some selected models where the transitions are well known: The 2D Ising, Potts and XY models and to a
homopolymer system. Our choices cover systems with first order, continuous and Berezinskii–Kosterlitz–
Thouless transitions as well as the homopolymer that has two pseudo-transitions. The strategy can easily
be adapted to any model, classical or quantum, once we are able to build the corresponding energy
probability distribution.
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Phase transitions, Monte carlo simulations, Partition function zeros
Citação
COSTA, B. V. da; MÓL, L. A. da S.; ROCHA, J. C. S. Energy probability distribution zeros: a route to study phase transitions. Computer Physics Communications, v. 216, p. 77-83, 2017. Disponível em: <http://www.sciencedirect.com/science/article/pii/S0010465517300796>. Acesso em: 16 jan. 2018.