Hybrid Monte Carlo algorithm for the Double Exchange Model

Details Hybrid Monte Carlo algorithm for the Double Exchange Model Hybrid Monte Carlo algorithm for the Double Exchange Model

2000-07-27

arxiv.org/abs/cond-mat/0007450v1

Nucl.Phys. B596 (2001) 587-610

Physics

Condensed Matter

Strongly Correlated Electrons

20 pages plus 4 postscript figures

Scientific paper

10.1016/S0550-3213(00)00681-7

The Hybrid Monte Carlo algorithm is adapted to the simulation of a system of classical degrees of freedom coupled to non self-interacting lattices fermions. The diagonalization of the Hamiltonian matrix is avoided by introducing a path-integral formulation of the problem, in $d+1$ Euclidean space-time. A perfect action formulation allows to work on the continuum euclidean time, without need for a Trotter-Suzuki extrapolation. To demonstrate the feasibility of the method we study the Double Exchange Model in three dimensions. The complexity of the algorithm grows only as the system volume, allowing to simulate in lattices as large as $16^3$ on a personal computer. We conclude that the second order paramagnetic-ferromagnetic phase transition of Double Exchange Materials close to half-filling belongs to the Universality Class of the three-dimensional classical Heisenberg model.

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